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

2 Answers
Feb 1, 2018

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

Feb 1, 2018

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 7xs 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.