Question

Solve the system of equations using elimination: -x+3y=-24− and -4x+2y=4

Answer 1

`\left \{ {{x=-6} \atop {y=-10}} \right. .`

Explanation:

`\left \{ {{-x+3y=-24\ \ (1)} \atop {-4x+2y=4\ \ \ (2)}} \right. \ \ \ \ \\`

We multiply equation (1) by -4:

-x+3y=-24 |*(-4)

-x*(-4)+3y*(-4)=-24*-(-4)

4x-12y=96. (3) ⇒

`\left \{ {{4x-12y=96\ \ (3)} \atop {-4x+2y=4\ \ \ (2)}} \right.`

We summarize equations (2) and (3):

`-10y=100\ |:(-10)\\y=-10.\\Make\ y \ the\ subject\ in\ (1):\\-x+3*(-10)=-24\\-x-30=-24\\-x=-24+30\\-x=6\ |*(-1)\\x=-6.`

Answer 2

`\begin{cases}x=-6\\y=-10\end`

Explanation:

`\begin{cases}-x+3y=-24 \left(1)\right\\-4x+2y=4 \left(2)\right\end`

Make x the subject in (1)

`x=3y+24 \left(3)\right`

Sub into (2)

`-4(3y+24)+2y=4\\\\\implies-12y-96+2y=4\\\\\implies10y=-100\\\\y=-10`

Sub into (3)

`x=-30+24\\\\x=-6`

Hence

`\begin{cases}x=-6\\y=-10\end`