Question

How do you solve the system of equations `-3x + 2y = - 15` and `2x = 4y + 26`?

Answer 1

`x=1; y=-6`

Explanation:

equation `(1)` is `-3x+2y=-15` and
equation `(2)` is `2x=4y+26.`

From equation `(2)`, we can divide by 2 and write:

equation `(3)` as `2y = x-13`

Substitute into equation `(1)` to give:

`-3x+(x-13) = -15;` which means `x=1`.

Now, sub `x=1` into equation `(3)`,

`2y = 1-13`,
`2y =-12`

`y = -6`

Answer 2

`x=1 and y =-6`

Explanation:

`color(white)(.....)-3x+2y =-15" "A`
`color(white)(.....)+2x-4y =+26" "B`

Try to create additive inverses with the variables.

`A xx 2: rarr color(white)(...)-6xcolor(blue)(+4y) =-30" "C`
`color(white)(........... ............)2xcolor(blue)(-4y) =+26" "B`

`C+B:color(white)(........)-4x " "= -4`
`color(white)(....................................)x =1`

Substitute `x=1` into B

`color(white)(.....)+2x-4y =+26" "B`
`color(white)(.....)+2(1)-4y =+26`
`color(white)(..........)+2-4y =+26`
`color(white)(.................)-4y =+26-2`
`color(white)(.................)-4y =+24`
`color(white)(.........................)y =-6`

Check in equation A:

`-3(1) +2(-6) = -15`
`-3-12 = -15`
`color(white)(......)-15 = -15`