Chapter 10

For Problems \(1-28\), (a) graph each system so that approximate real number solutions (if there are any) can be predicted, and (b) solve each system using the substitution method or the elimination-by-addition method. (Objectives 1 and 2) $$ \left(\begin{array}{l} y=(x+2)^{2} \\ y=-2 x-4 \end{array}\right) $$

For Problems \(1-10\), use expansion by minors to evaluate each determinant. (Objective 1) $$ \left|\begin{array}{rrr} 2 & 7 & 5 \\ 1 & -1 & 1 \\ -4 & 3 & 2 \end{array}\right| $$

Evaluate each of the following determinants. $$ \left|\begin{array}{ll} 6 & 2 \\ 4 & 3 \end{array}\right| $$

For Problems \(1-22\), solve each of the systems and use matrices as we did in the examples of this section. $$ \left(\begin{array}{rr} x-2 y= & 14 \\ 4 x+5 y= & 4 \end{array}\right) $$

Solve each of the following systems. If the solution set is \(\varnothing\) or if it contains infinitely many solutions, then so indicate. $$ \left(\begin{array}{rr} x+2 y-3 z= & 2 \\ 3 y-z= & 13 \\ 3 y+5 z= & 25 \end{array}\right) $$

For Problems \(1-18\), use the elimination-by-addition method to solve each system. (Objective 1 ) $$ \left(\begin{array}{l} 2 x+3 y=-1 \\ 5 x-3 y=29 \end{array}\right) $$

For Problems \(1-26\), solve each system by using the substitution method. (Objective 1) $$ \left(\begin{array}{l} x+y=20 \\ x=y-4 \end{array}\right) $$

For Problems \(1-16\), use the graphing approach to determine whether the system is consistent, the system is inconsistent, or the equations are dependent. If the system is consistent, find the solution set from the graph and check it. (Objective 1) $$ \left(\begin{array}{r} x-y=1 \\ 2 x+y=8 \end{array}\right) $$

For Problems \(1-28\), (a) graph each system so that approximate real number solutions (if there are any) can be predicted, and (b) solve each system using the substitution method or the elimination-by-addition method. (Objectives 1 and 2) $$ \left(\begin{array}{l} y=x-1 \\ x=(y-1)^{2} \end{array}\right) $$

For Problems \(1-10\), use expansion by minors to evaluate each determinant. (Objective 1) $$ \left|\begin{array}{rrr} 2 & 4 & 1 \\ -1 & 5 & 1 \\ -3 & 6 & 2 \end{array}\right| $$

Evaluate each of the following determinants. $$ \left|\begin{array}{ll} 7 & 6 \\ 2 & 5 \end{array}\right| $$

Solve each of the following systems. If the solution set is \(\varnothing\) or if it contains infinitely many solutions, then so indicate. $$ \left(\begin{array}{rr} 2 x+3 y-4 z & =-10 \\ 2 y+3 z & =16 \\ 2 y-5 z & =-16 \end{array}\right) $$

For Problems \(1-18\), use the elimination-by-addition method to solve each system. (Objective 1 ) $$ \left(\begin{array}{l} 3 x-4 y=-30 \\ 7 x+4 y=10 \end{array}\right) $$

For Problems \(1-26\), solve each system by using the substitution method. (Objective 1) $$ \left(\begin{array}{l} x+y=23 \\ y=x-5 \end{array}\right) $$

For Problems \(1-16\), use the graphing approach to determine whether the system is consistent, the system is inconsistent, or the equations are dependent. If the system is consistent, find the solution set from the graph and check it. (Objective 1) $$ \left(\begin{array}{c} 3 x+y=0 \\ x-2 y=-7 \end{array}\right) $$

For Problems \(1-10\), use expansion by minors to evaluate each determinant. (Objective 1) $$ \left|\begin{array}{rrr} 3 & -2 & 1 \\ 2 & 1 & 4 \\ -1 & 3 & 5 \end{array}\right| $$

Evaluate each of the following determinants. $$ \left|\begin{array}{ll} 4 & 7 \\ 8 & 2 \end{array}\right| $$

Solve each of the following systems. If the solution set is \(\varnothing\) or if it contains infinitely many solutions, then so indicate. $$ \left(\begin{array}{rr} 3 x+2 y-2 z= & 14 \\ x+6 z= & 16 \\ 2 x+5 z= & -2 \end{array}\right) $$

For Problems \(1-18\), use the elimination-by-addition method to solve each system. (Objective 1 ) $$ \left(\begin{array}{l} 6 x-7 y=15 \\ 6 x+5 y=-21 \end{array}\right) $$

For Problems \(1-26\), solve each system by using the substitution method. (Objective 1) $$ \left(\begin{array}{l} y=-3 x-18 \\ 5 x-2 y=-8 \end{array}\right) $$

For Problems \(1-16\), use the graphing approach to determine whether the system is consistent, the system is inconsistent, or the equations are dependent. If the system is consistent, find the solution set from the graph and check it. (Objective 1) $$ \left(\begin{array}{l} 4 x+3 y=-5 \\ 2 x-3 y=-7 \end{array}\right) $$

For Problems \(1-28\), (a) graph each system so that approximate real number solutions (if there are any) can be predicted, and (b) solve each system using the substitution method or the elimination-by-addition method. (Objectives 1 and 2) $$ \left(\begin{array}{l} y=x^{2} \\ y=x+2 \end{array}\right) $$

For Problems \(1-10\), use expansion by minors to evaluate each determinant. (Objective 1) $$ \left|\begin{array}{rrr} 1 & -1 & 2 \\ 2 & 1 & 3 \\ -1 & -2 & 1 \end{array}\right| $$

Evaluate each of the following determinants. $$ \left|\begin{array}{ll} 3 & 9 \\ 6 & 4 \end{array}\right| $$

For Problems \(1-22\), solve each of the systems and use matrices as we did in the examples of this section. $$ \left(\begin{array}{r} 7 x-9 y=53 \\ x-3 y=11 \end{array}\right) $$

Solve each of the following systems. If the solution set is \(\varnothing\) or if it contains infinitely many solutions, then so indicate. $$ \left(\begin{array}{rl} 3 x+2 y-z & =-11 \\ 2 x-3 y & =-1 \\ 4 x+5 y & =-13 \end{array}\right) $$

For Problems \(1-18\), use the elimination-by-addition method to solve each system. (Objective 1 ) $$ \left(\begin{array}{l} 5 x+2 y=-4 \\ 5 x-3 y=6 \end{array}\right) $$

For Problems \(1-26\), solve each system by using the substitution method. (Objective 1) $$ \left(\begin{array}{l} 4 x-3 y=33 \\ x=-4 y-25 \end{array}\right) $$

For Problems \(1-16\), use the graphing approach to determine whether the system is consistent, the system is inconsistent, or the equations are dependent. If the system is consistent, find the solution set from the graph and check it. (Objective 1) $$ \left(\begin{array}{c} 2 x-y=9 \\ 4 x-2 y=11 \end{array}\right) $$

For Problems \(1-28\), (a) graph each system so that approximate real number solutions (if there are any) can be predicted, and (b) solve each system using the substitution method or the elimination-by-addition method. (Objectives 1 and 2) $$ \left(\begin{array}{lr} x^{2}+y^{2}= & 13 \\ 3 x+2 y= & 0 \end{array}\right) $$

For Problems \(1-10\), use expansion by minors to evaluate each determinant. (Objective 1) $$ \left|\begin{array}{rrr} -3 & -2 & 1 \\ 5 & 0 & 6 \\ 2 & 1 & -4 \end{array}\right| $$

Evaluate each of the following determinants. $$ \left|\begin{array}{rr} -3 & 2 \\ 7 & 5 \end{array}\right| $$

Solve each of the following systems. If the solution set is \(\varnothing\) or if it contains infinitely many solutions, then so indicate. $$ \left(\begin{array}{rr} 2 x-y+z= & 0 \\ 3 x-2 y+4 z= & 11 \\ 5 x+y-6 z= & -32 \end{array}\right) $$

For Problems \(1-18\), use the elimination-by-addition method to solve each system. (Objective 1 ) $$ \left(\begin{array}{rr} x-2 y= & -12 \\ 2 x+9 y= & 2 \end{array}\right) $$

For Problems \(1-26\), solve each system by using the substitution method. (Objective 1) $$ \left(\begin{array}{l} x=-3 y \\ 7 x-2 y=-69 \end{array}\right) $$

For Problems \(1-16\), use the graphing approach to determine whether the system is consistent, the system is inconsistent, or the equations are dependent. If the system is consistent, find the solution set from the graph and check it. (Objective 1) $$ \left(\begin{array}{l} \frac{1}{2} x+\frac{1}{4} y=9 \\ 4 x+2 y=72 \end{array}\right) $$

For Problems \(1-28\), (a) graph each system so that approximate real number solutions (if there are any) can be predicted, and (b) solve each system using the substitution method or the elimination-by-addition method. (Objectives 1 and 2) $$ \left(\begin{array}{l} x^{2}+y^{2}=26 \\ x+y=6 \end{array}\right) $$

For Problems \(1-10\), use expansion by minors to evaluate each determinant. (Objective 1) $$ \left|\begin{array}{rrr} -5 & 1 & -1 \\ 3 & 4 & 2 \\ 0 & 2 & -3 \end{array}\right| $$

Evaluate each of the following determinants. $$ \left|\begin{array}{rr} 5 & 1 \\ 8 & -4 \end{array}\right| $$

Solve each of the following systems. If the solution set is \(\varnothing\) or if it contains infinitely many solutions, then so indicate. $$ \left(\begin{array}{rr} x-2 y+3 z= & 7 \\ 2 x+y+5 z= & 17 \\ 3 x-4 y-2 z= & 1 \end{array}\right) $$

For Problems \(1-18\), use the elimination-by-addition method to solve each system. (Objective 1 ) $$ \left(\begin{array}{rr} x-4 y= & 29 \\ 3 x+2 y= & -11 \end{array}\right) $$

For Problems \(1-26\), solve each system by using the substitution method. (Objective 1) $$ \left(\begin{array}{l} 9 x-2 y=-38 \\ y=-5 x \end{array}\right) $$

For Problems \(1-16\), use the graphing approach to determine whether the system is consistent, the system is inconsistent, or the equations are dependent. If the system is consistent, find the solution set from the graph and check it. (Objective 1) $$ \left(\begin{array}{l} 5 x+2 y=-9 \\ 4 x-3 y=2 \end{array}\right) $$

For Problems \(1-28\), (a) graph each system so that approximate real number solutions (if there are any) can be predicted, and (b) solve each system using the substitution method or the elimination-by-addition method. (Objectives 1 and 2) $$ \left(\begin{array}{rl} y & =\frac{5}{2} x \\ x^{2}+y^{2} & =29 \end{array}\right) $$

For Problems \(1-10\), use expansion by minors to evaluate each determinant. (Objective 1) $$ \left|\begin{array}{rrr} 3 & -4 & -2 \\ 5 & -2 & 1 \\ 1 & 0 & 0 \end{array}\right| $$

Evaluate each of the following determinants. $$ \left|\begin{array}{rr} 8 & -3 \\ 6 & 4 \end{array}\right| $$

Solve each of the following systems. If the solution set is \(\varnothing\) or if it contains infinitely many solutions, then so indicate. $$ \left(\begin{array}{r} 4 x-y+z=5 \\ 3 x+y+2 z=4 \\ x-2 y-z=1 \end{array}\right) $$

For Problems \(1-18\), use the elimination-by-addition method to solve each system. (Objective 1 ) $$ \left(\begin{array}{l} 4 x+7 y=-16 \\ 6 x-y=-24 \end{array}\right) $$

For Problems \(1-26\), solve each system by using the substitution method. (Objective 1) $$ \left(\begin{array}{l} 2 x+3 y=11 \\ 3 x-2 y=-3 \end{array}\right) $$

For Problems \(1-16\), use the graphing approach to determine whether the system is consistent, the system is inconsistent, or the equations are dependent. If the system is consistent, find the solution set from the graph and check it. (Objective 1) $$ \left(\begin{array}{rl} \frac{1}{2} x-\frac{1}{3} y & =3 \\ x+4 y & =-8 \end{array}\right) $$