Question

Solve using elimination.–2x − 7y = 9x − 7y = –15

Answer 1

The question wants us to solve the following system of equations by elimination:

`\begin{gathered} -2x-7=9 \\ x-7y=-15 \end{gathered}`

Solution

`\begin{gathered} -2x-7y=9\text{ (Equation 1)} \\ x-7y=-15\text{ (Equation 2)} \\ \\ \text{Subtract both equations} \\ -2x-7y-(x-7y)=9-(-15) \\ -2x-7y-x+7y=9+15 \\ -2x-x-7y+7y=24 \\ -3x=24 \\ \text{Divide both sides by -3} \\ -(3x)/(-3)=(24)/(-3) \\ \\ \therefore x=-8 \\ \\ \text{Substitute the value for x into Equation 1}.\text{ This will help us find y.} \\ -2x-7y=9 \\ -2(-8)-7y=9 \\ 16-7y=9 \\ \text{Subtract 16 from both sides} \\ -7y=9-16 \\ -7y=-7 \\ \text{Divide both sides by -7} \\ -(7y)/(-7)=-(7)/(-7) \\ \\ \therefore y=1 \end{gathered}`

Answer

The answer to the system of equations is:

x = -8

y = 1