Answer
The solution to this system of equations is $(1, 2)$.
Work Step by Step
To solve this system of equations by substitution, we solve one of the equations in terms of one variable.
Use the "simpler" equation, which is the second one where $y$ is easy to isolate:
$2x + y = 4$
Subtract $2x$ from each side to isolate $y$:
$y = 4 - 2x$
Use this value for $y$ to plug in to the first equation to obtain the value for $x$:
$3x + 5(4 - 2x) = 13$
Use distribution to get rid of the parentheses:
$3x + 20 - 10x = 13$
Subtract $20$ from both sides of the equation to isolate constants to the right side of the equation:
$3x - 10x = -7$
Subtract like terms on the left side of the equation:
$-7x = -7$
Divide both sides by $-7$ to solve for $x$:
$x = 1$
Substitute $x=-1$ into the second equation to solve for $y$:
$2(1) + y = 4$
$2 + y = 4$
Subtract $2$ from each side of the equation to solve for $y$:
$y = 2$
The solution to this system of equations is $(1, 2)$.
