Chapter 5

Determine the Number of Solutions of a Linear System Without graphing the following systems of equations, determine the number of solutions and then classify the system of equations. $$ \left\\{\begin{array}{l} y=-2 x+1 \\ 4 x+2 y=8 \end{array}\right. $$

Determine the Number of Solutions of a Linear System Without graphing the following systems of equations, determine the number of solutions and then classify the system of equations. $$ \left\\{\begin{array}{l} y=3 x+4 \\ 9 x-3 y=18 \end{array}\right. $$

Determine the Number of Solutions of a Linear System Without graphing the following systems of equations, determine the number of solutions and then classify the system of equations. $$ \left\\{\begin{array}{l} y=\frac{2}{3} x+1 \\ 2 x-3 y=7 \end{array}\right. $$

Determine the Number of Solutions of a Linear System Without graphing the following systems of equations, determine the number of solutions and then classify the system of equations. $$ \left\\{\begin{array}{l} 3 x+4 y=12 \\ y=-3 x-1 \end{array}\right. $$

Determine the Number of Solutions of a Linear System Without graphing the following systems of equations, determine the number of solutions and then classify the system of equations. $$ \left\\{\begin{array}{l} 4 x+2 y=10 \\ 4 x-2 y=-6 \end{array}\right. $$

Determine the Number of Solutions of a Linear System Without graphing the following systems of equations, determine the number of solutions and then classify the system of equations. $$ \left\\{\begin{array}{l} 5 x+3 y=4 \\ 2 x-3 y=5 \end{array}\right. $$

Determine the Number of Solutions of a Linear System Without graphing the following systems of equations, determine the number of solutions and then classify the system of equations. $$ \left\\{\begin{array}{l} y=-\frac{1}{2} x+5 \\ x+2 y=10 \end{array}\right. $$

Determine the Number of Solutions of a Linear System Without graphing the following systems of equations, determine the number of solutions and then classify the system of equations. $$ \left\\{\begin{array}{l} y=x+1 \\ -x+y=1 \end{array}\right. $$

Determine the Number of Solutions of a Linear System Without graphing the following systems of equations, determine the number of solutions and then classify the system of equations. $$ \left\\{\begin{array}{l} y=2 x+3 \\ 2 x-y=-3 \end{array}\right. $$

Determine the Number of Solutions of a Linear System Without graphing the following systems of equations, determine the number of solutions and then classify the system of equations. $$ \left\\{\begin{array}{l} 5 x-2 y=10 \\ y=\frac{5}{2} x-5 \end{array}\right. $$

Leo is planning his spring flower garden. He wants to plant tulip and daffodil bulbs. He will plant 6 times as many daffodil bulbs as tulip bulbs. If he wants to plant 350 bulbs, how many tulip bulbs and how many daffodil bulbs should he plant?

A marketing company surveys 1,200 people. They surveyed twice as many females as males. How many males and females did they survey?

In the following exercises, solve the systems of equations by substitution. $$ \left\\{\begin{array}{l} 2 x+y=-4 \\ 3 x-2 y=-6 \end{array}\right. $$

In the following exercises, solve the systems of equations by substitution. $$ \left\\{\begin{array}{l} 2 x+y=-2 \\ 3 x-y=7 \end{array}\right. $$

In the following exercises, solve the systems of equations by substitution. $$ \left\\{\begin{array}{l} x-2 y=-5 \\ 2 x-3 y=-4 \end{array}\right. $$

In the following exercises, solve the systems of equations by substitution. $$ \left\\{\begin{array}{l} x-3 y=-9 \\ 2 x+5 y=4 \end{array}\right. $$

In the following exercises, solve the systems of equations by substitution. $$ \left\\{\begin{array}{l} 5 x-2 y=-6 \\ y=3 x+3 \end{array}\right. $$

In the following exercises, solve the systems of equations by substitution. $$ \left\\{\begin{array}{l} -2 x+2 y=6 \\ y=-3 x+1 \end{array}\right. $$

In the following exercises, solve the systems of equations by substitution. $$ \left\\{\begin{array}{l} 2 x+3 y=3 \\ y=-x+3 \end{array}\right. $$

In the following exercises, solve the systems of equations by substitution. $$ \left\\{\begin{array}{l} 2 x+5 y=-14 \\ y=-2 x+2 \end{array}\right. $$

In the following exercises, solve the systems of equations by substitution. $$ \left\\{\begin{array}{l} 2 x+5 y=1 \\ y=\frac{1}{3} x-2 \end{array}\right. $$

In the following exercises, solve the systems of equations by substitution. $$ \left\\{\begin{array}{l} 3 x+4 y=1 \\ y=-\frac{2}{5} x+2 \end{array}\right. $$

In the following exercises, solve the systems of equations by substitution. $$ \left\\{\begin{array}{l} 3 x-2 y=6 \\ y=\frac{2}{3} x+2 \end{array}\right. $$

$$ \left\\{\begin{array}{l} -3 x-5 y=3 \\ y=\frac{1}{2} x-5 \end{array}\right. $$$$ \left\\{\begin{array}{l} -3 x-5 y=3 \\ y=\frac{1}{2} x-5 \end{array}\right. $$

In the following exercises, solve the systems of equations by substitution. $$ \left\\{\begin{array}{l} 2 x+y=10 \\ -x+y=-5 \end{array}\right. $$

In the following exercises, solve the systems of equations by substitution. $$ \left\\{\begin{array}{l} -2 x+y=10 \\ -x+2 y=16 \end{array}\right. $$

In the following exercises, solve the systems of equations by substitution. $$ \left\\{\begin{array}{l} 3 x+y=1 \\ -4 x+y=15 \end{array}\right. $$

In the following exercises, solve the systems of equations by substitution. $$ \left\\{\begin{array}{l} x+y=0 \\ 2 x+3 y=-4 \end{array}\right. $$

In the following exercises, solve the systems of equations by substitution. $$ \left\\{\begin{array}{l} x+3 y=1 \\ 3 x+5 y=-5 \end{array}\right. $$

In the following exercises, solve the systems of equations by substitution. $$ \left\\{\begin{array}{l} x+2 y=-1 \\ 2 x+3 y=1 \end{array}\right. $$

In the following exercises, solve the systems of equations by substitution. $$ \left\\{\begin{array}{l} 2 x+y=5 \\ x-2 y=-15 \end{array}\right. $$

In the following exercises, solve the systems of equations by substitution. $$ \left\\{\begin{array}{l} 4 x+y=10 \\ x-2 y=-20 \end{array}\right. $$

In the following exercises, solve the systems of equations by substitution. $$ \left\\{\begin{array}{l} y=-2 x-1 \\ y=-\frac{1}{3} x+4 \end{array}\right. $$

In the following exercises, solve the systems of equations by substitution. $$ \left\\{\begin{array}{l} y=x-6 \\ y=-\frac{3}{2} x+4 \end{array}\right. $$

In the following exercises, solve the systems of equations by substitution. $$ \left\\{\begin{array}{l} y=2 x-8 \\ y=\frac{3}{5} x+6 \end{array}\right. $$

In the following exercises, solve the systems of equations by substitution. $$ \left\\{\begin{array}{l} y=-x-1 \\ y=x+7 \end{array}\right. $$

In the following exercises, solve the systems of equations by substitution. $$ \left\\{\begin{array}{l} 4 x+2 y=8 \\ 8 x-y=1 \end{array}\right. $$

$$ \left\\{\begin{array}{l} -x-12 y=-1 \\ 2 x-8 y=-6 \end{array}\right. $$$$ \left\\{\begin{array}{l} -x-12 y=-1 \\ 2 x-8 y=-6 \end{array}\right. $$

In the following exercises, solve the systems of equations by substitution. $$ \left\\{\begin{array}{l} 15 x+2 y=6 \\ -5 x+2 y=-4 \end{array}\right. $$

$$ \left\\{\begin{array}{l} 2 x-15 y=7 \\ 12 x+2 y=-4 \end{array}\right. $$$$ \left\\{\begin{array}{l} 2 x-15 y=7 \\ 12 x+2 y=-4 \end{array}\right. $$

In the following exercises, solve the systems of equations by substitution. $$ \left\\{\begin{array}{l} y=3 x \\ 6 x-2 y=0 \end{array}\right. $$

In the following exercises, solve the systems of equations by substitution. $$ \left\\{\begin{array}{l} x=2 y \\ 4 x-8 y=0 \end{array}\right. $$

In the following exercises, solve the systems of equations by substitution. $$ \left\\{\begin{array}{l} 2 x+16 y=8 \\ -x-8 y=-4 \end{array}\right. $$

In the following exercises, solve the systems of equations by substitution. $$ \left\\{\begin{array}{l} 15 x+4 y=6 \\ -30 x-8 y=-12 \end{array}\right. $$

In the following exercises, solve the systems of equations by substitution. $$ \left\\{\begin{array}{l} y=-4 x \\ 4 x+y=1 \end{array}\right. $$

In the following exercises, solve the systems of equations by substitution. $$ \left\\{\begin{array}{l} y=-\frac{1}{4} x \\ x+4 y=8 \end{array}\right. $$

In the following exercises, solve the systems of equations by substitution. $$ \left\\{\begin{array}{l} y=\frac{7}{8} x+4 \\ -7 x+8 y=6 \end{array}\right. $$

In the following exercises, solve the systems of equations by substitution. $$ \left\\{\begin{array}{l} y=-\frac{2}{3} x+5 \\ 2 x+3 y=11 \end{array}\right. $$

The sum of two numbers is 15. One number is 3 less than the other. Find the numbers.

The sum of two numbers is 30. One number is 4 less than the other. Find the numbers.