Question

=-=Solve this system of equations by usingthe elimination method.+x+ 5y = 29 Combine the equationsto eliminate the xx - 2y = -8variable.0 + [?]y =Hint: Add together 5ý and (-2y).Enter the new coefficient of y.=

Answer 1

`\begin{gathered} x=6 \\ y=7 \end{gathered}`

Step-by-step explanation

`\begin{gathered} -x+5y=29 \\ x-2y=-8 \end{gathered}`

Step 1

a) add the equations to eliminate the x variable

`\begin{gathered} -x+5y=29 \\ x-2y=-8 \\ _{\text{ + \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_}} \\ \lparen x-x)+\left(5-2\right)y=\left(29-8\right) \\ 0+3y=21\Rightarrow blanks \\ \end{gathered}`

Step 2

`0+3y=21`

divide both sides by 3

`\begin{gathered} (3y)/(3)=(21)/(3) \\ y=7 \end{gathered}`

so

y=7

Step 3

finally, replace the y value in equation (1) and solve for x

`\begin{gathered} -x+5y=29 \\ replace \\ -x-5*7=29 \\ -x+35=29 \\ subtract\text{ 35 in both sides} \\ -x+35-35=29-35 \\ -x=-6 \\ x=6 \end{gathered}`

so,

x=6

therefore, the solution to the system of equations is

`\begin{gathered} x=6 \\ y=7 \end{gathered}`

I hope this helps you