How do you solve the system of equations 5x - 6y = 9 and 5x + 2y = 19?

1 Answer
Mar 22, 2017

The final solution is x = 3 3/10 and y = 1 1/4 using substitution to solve the system of equations.

Explanation:

We notice that in both equations, there is a 5x. This suggests using elimination to solve the equations.

Since the equations have the same term with one of the variables (5x), we can subtract the two equations to eliminate x and leave one equation to solve for y. Subtracting the first equation from the second and solving gives us:

2y - (-6y) = 19 - 9

8y = 10

y = 5/4

Now, we can simply substitute the value of y into any of the 2 equations to solve for x. Substituting into the second equation and solving, we get:

5x + 2(5/4) = 19

5x + 5/2 = 19

5x = 33/2

x = 33/10

So, the answer to the equations is x = 3 3/10 and y = 1 1/4.