Chapter 7

Graph the system of linear inequalities. $$ \begin{aligned} &y>-2\\\ &y \leq 4-2 x \end{aligned} $$

Choose a solution method to solve the linear system. Explain your choice, but do not solve the system. $$ \begin{aligned} &2 x+3 y=3\\\ &5 x+5 y=10 \end{aligned} $$

Use linear combinations to solve the linear system. Then check your solution. \(g+2 h=4\) \(-g-h=2\)

Tell which equation you would use to isolate a variable. Explain. $$ \begin{array}{r} {4 a+3 b=-5} \\ {a-b=-3} \end{array} $$

Graph the system of linear inequalities. $$ \begin{aligned} &2 x+3 y<5\\\ &3 x+2 y>5 \end{aligned} $$

Choose a solution method to solve the linear system. Explain your choice, but do not solve the system. $$ \begin{aligned} -3 x &=36 \\ -6 x+y &=1 \end{aligned} $$

Use linear combinations to solve the linear system. Then check your solution. $$ \begin{array}{r} 13 x-5 y=8 \\ 3 x+5 y=8 \end{array} $$

Tell which equation you would use to isolate a variable. Explain. $$ \begin{aligned} 3 x+5 y &=25 \\ x-2 y &=-10 \end{aligned} $$

Graph the system of linear inequalities. $$ \begin{aligned} &y<2 x-1\\\ &y>-x+2 \end{aligned} $$

Choose a solution method to solve the linear system. Explain your choice, but do not solve the system. $$ \begin{array}{r} {2 x-5 y=0} \\ {x-y=3} \end{array} $$

Use linear combinations to solve the linear system. Then check your solution. \(x+3 y=3\) \(x+6 y=3\)

Estimate the solution of the linear system graphically. Then check the solution algebraically. $$ \begin{aligned} &y=-x+3\\\ &y=x+1 \end{aligned} $$

Use the substitution method to solve the linear system. $$ \begin{aligned} &y=x-4\\\ &4 x+y=26 \end{aligned} $$

Graph the system of linear inequalities. $$ \begin{array}{r} {2 x-2 y \leq 6} \\ {x-y \leq 9} \end{array} $$

Choose a solution method to solve the linear system. Explain your choice, but do not solve the system. $$ \begin{aligned} &3 x+2 y=10\\\ &2 x+5 y=3 \end{aligned} $$

Use linear combinations to solve the linear system. Then check your solution. \(v-w=-5\) \(v+2 w=4\)

Estimate the solution of the linear system graphically. Then check the solution algebraically. $$ \begin{aligned} &y=-6\\\ &x=6 \end{aligned} $$

Use the substitution method to solve the linear system. $$ \begin{aligned} &s=t+4\\\ &2 t+s=19 \end{aligned} $$

Graph the system of linear inequalities. $$ \begin{aligned} &x-3 y \geq 12\\\ &x-6 y<12 \end{aligned} $$

Use the graphing method to tell how many solutions the system has. $$\begin{aligned} &x+y=8\\\ &x+y=-1 \end{aligned}$$

Choose a solution method to solve the linear system. Explain your choice, but do not solve the system. $$ \begin{aligned} &x+2 y=2\\\ &x+4 y=-2 \end{aligned} $$

Use linear combinations to solve the linear system. Then check your solution. \(2 g-3 h=0\) \(3 g-2 h=5\)

Estimate the solution of the linear system graphically. Then check the solution algebraically. $$ \begin{array}{c} {y=2 x-4} \\ {2 y=-x} \end{array} $$

Use the substitution method to solve the linear system. $$ \begin{aligned} &2 c-d=-2\\\ &4 c+d=20 \end{aligned} $$

Graph the system of linear inequalities. $$ \begin{array}{r} {x+y \leq 6} \\ {x \geq 1} \\ {y \geq 0} \end{array} $$

Choose a solution method to solve the linear system. Explain your choice, and then solve the system. $$ \begin{array}{r} {2 x+y=5} \\ {x-y=1} \end{array} $$

Use the graphing method to tell how many solutions the system has. $$\begin{aligned} 3 x-2 y &=3 \\ -6 x+4 y &=-6 \end{aligned}$$

Use linear combinations to solve the linear system. Then check your solution. \(x-y=0\) \(-3 x-y=2\)

Estimate the solution of the linear system graphically. Then check the solution algebraically. $$ \begin{array}{r} {2 x-3 y=9} \\ {x=-3} \end{array} $$

Use the substitution method to solve the linear system. $$ \begin{array}{r} {2 a=8} \\ {a+b=2} \end{array} $$

Graph the system of linear inequalities. $$ \begin{array}{r} {x<3} \\ {2 y<1} \\ {2 x+y>2} \end{array} $$

Use the graphing method to tell how many solutions the system has. $$\begin{array}{r} {x-y=2} \\ {-2 x+2 y=2} \end{array}$$

Choose a solution method to solve the linear system. Explain your choice, and then solve the system. $$ \begin{array}{c} {2 x-y=3} \\ {4 x+3 y=21} \end{array} $$

Use linear combinations to solve the linear system. Then check your solution. \(2 a+6 z=4\) \(3 a-7 z=6\)

Estimate the solution of the linear system graphically. Then check the solution algebraically. $$ \begin{aligned} 5 x+4 y &=16 \\ y &=-16 \end{aligned} $$

Use the substitution method to solve the linear system. $$ \begin{aligned} &2 x+3 y=31\\\ &y=x+7 \end{aligned} $$

Graph the system of linear inequalities. $$ \begin{array}{c} {3 x-2 y \geq-6} \\ {x+4 y>-2} \\ {4 x+y<2} \end{array} $$

Choose a solution method to solve the linear system. Explain your choice, and then solve the system. $$ \begin{array}{c} {x-2 y=4} \\ {6 x+2 y=10} \end{array} $$

Use the graphing method to tell how many solutions the system has. $$\begin{aligned} -x+4 y &=-20 \\ 3 x-12 y &=48 \end{aligned}$$

Use linear combinations to solve the linear system. Then check your solution. \(5 e+4 f=9\) \(4 e+5 f=9\)

Estimate the solution of the linear system graphically. Then check the solution algebraically. $$ \begin{array}{r} {x-y=1} \\ {5 x-4 y=0} \end{array} $$

Use the substitution method to solve the linear system. $$ \begin{array}{c} {p+q=4} \\ {4 p+q=1} \end{array} $$

Graph the system of linear inequalities. $$ \begin{aligned} &x \geq 0\\\ &y \geq 0\\\ &x \leq 3 \end{aligned} $$

Use the graphing method to tell how many solutions the system has. $$\begin{array}{r} {6 x-2 y=4} \\ {12 x-6 y=8} \end{array}$$

Choose a solution method to solve the linear system. Explain your choice, and then solve the system. $$ \begin{array}{r} {3 x+6 y=8} \\ {-6 x+3 y=2} \end{array} $$

Use linear combinations to solve the linear system. Then check your solution. \(2 p-q=2\) \(2 p+3 q=22\)

Estimate the solution of the linear system graphically. Then check the solution algebraically. $$ \begin{array}{r} {3 x+6 y=15} \\ {-2 x+3 y=-3} \end{array} $$

Use the substitution method to solve the linear system. $$ \begin{aligned} &x-2 y=-25\\\ &3 x-y=0 \end{aligned} $$

Graph the system of linear inequalities. $$ \begin{aligned} &x>-2\\\ &y \geq-2\\\ &y<4 \end{aligned} $$

Use the graphing method to tell how many solutions the system has. $$\begin{aligned} 3 x+2 y &=40 \\ -3 x-2 y &=8 \end{aligned}$$