Question

How do you combine the system of equations `7x - 9y = 2` and `7x + 3y = - 10`?

Answer 1

`color(blue)(14x - 6y = -8`

Explanation:

Given :

`color(green)(7x - 9y = 2` Equation (1)

`color(green)(7x + 3y = -10` Equation (2)

Add equations (1), (2). We get

`L H S = 7x - 9y + 7x + 3y`

Rearranging like terms together,

`L H S = 7x + 7x - 9y + 3y = 14x - 6y`

Similarly,
`R H S = 2 + (-10) = 2 - 10 = -8`

But L H S = R H S.

`:. color(blue)(14x - 6y = -8`

Answer 2

`y = -1`

Explanation:

The primary idea of combining a system of equations is that one term cancels out, leaving a single one-variable equation. For example, in this case, you can easily see that both equations have a `7x` term. This means that if you subtract one equation from another, the `7x`s will cancel out, leaving an equation with only a `y` term.

`7x−9y=2`
`-`
`7x+3y=-10`
`------`
`0x-12y=12`
From here, divide by -12:
`y = -1`
If you want to find the solution to the ordered pair, then substitute the y into one of the original equations.

Note: this could also work if you wanted to cancel out the `y` terms - it just would take a little more algebra and create some fractions.