How do you solve the following system: 5x + 8y = -2, 6x+3y=-12?

1 Answer
Shantelle
Oct 20, 2017

The solution for the system is (-4.18, 2.36).

Explanation:

First, we want to make either x or y by itself, so that later we can plug it back into the equation.

So the 2 equations are 5x + 8y = -2 and 6x + 3y = -12.

Let's solve for y first using the 6x + 3y = -12 equation

2x + y = -6 (divide everything by 3)

y = -6 - 2x

Now, we plug in the value we just got for y back into the first equation, 5x + 8y = -2. We solve for x here.

5x + 8(-6 - 2x) = -2 (plug in value for y)

5x - 48 - 16x = -2 (distribute)

-11x = 46 (simplify, put all unknowns on one side, everything else on right side of equation)

x = -4.1818... ~~ -4.18 (rounded to hundredth's place)

Since we now know the value of x, we can plug that value back into the equation, y = -6 - 2x to solve for y.

y = -6 - 2(-4.18) (plug in value for x

y = -6 + 8.36

y = 2.36

The solution is the (x, y) coordinate.
We know x ~~ -4.18 and y ~~ 2.36, so:
Final answer: The solution for the system is (-4.18, 2.36).

Related questions
See all questions in Systems Using Substitution
Impact of this question
1763 views around the world
You can reuse this answer
Creative Commons License