Answer
The solution to this system of equations is $(3, -1)$.
Work Step by Step
We can use the substitution method to solve this system of equations because one of the equations already has the $y$ term isolated. We can use this second equation to substitute for $y$ in the first equation:
$$5x + 2(2x - 7) = 13$$
Use distributive property to simplify and get rid of the parentheses:
$$5x + (2)(2x) + (2)(-7) = 13$$
Multiply the terms:
$$5x + 4x - 14 = 13$$
Group like terms:
$$(5x + 4x) - 14 = 13$$
Combine like terms:
$$9x - 14 = 13$$
Add $14$ to each side to isolate the constants to one side of the equation:
$$9x = 27$$
Divide both sides of the equation by $9$ to solve for $x$:
$$x = 3$$
We plug $3$ in for $x$ in the second equation to find $y$:
$$y = 2(3) - 7$$
Multiply first, according to order of operations:
$$y = 6 - 7$$
Subtract to solve for $y$:
$$y = -1$$
The solution to this system of equations is $(3, -1)$.
