Question

---Solve the system of equations --5x + 9y = -37 and -x + 2y = -9 bycombining the equations.

Answer 1

Given the equations:

`\begin{gathered} -5x+9y=-37 \\ -x+2y=-9 \end{gathered}`

Solve for x in the second equation:

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

Multiply by (-1) on both sides:

`\begin{gathered} \lparen-1)(-x)=(-1)(-9-2y) \\ x=9+2y \end{gathered}`

Substitute x in the first equation:

`-5(9+2y)+9y=-37`

Simplify:

`\begin{gathered} -45-10y+9y=-37 \\ -45-y=-37 \end{gathered}`

Solve for y:

`\begin{gathered} -45-y+45=-37+45 \\ -y=8 \\ (-y)/(-1)=(8)/(-1) \\ y=-8 \end{gathered}`

Then, substitute y = -8 and solve for x:

`x=9+2(-8)=9-16=-7`

Answer:

x = -7

y = -8