Question

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

Answer 1

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`.