Answer
The solutions is $(3, 3)$.
Work Step by Step
Since we have an equation where the $y$ term is already isolated, we can use the substitution method for this system of equations.
We use $y = 2x - 3$ to substitute for $y$ in the second equation:
$$x + 2(2x - 3) = 9$$
Distribute first, according to order of operations:
$$x + 2(2x) + (2)(-3) = 9$$
Multiply the terms to simplify:
$$x + 4x - 6 = 9$$
Group like terms:
$$(x + 4x) - 6 = 9$$
Combine like terms:
$$5x - 6 = 9$$
Add $6$ to both sides to isolate the constants to one side of the equation:
$$5x = 15$$
Divide both sides by $5$ to solve for $x$:
$$x = 3$$
We can now plug $3$ in for $x$ into the first equation to solve for $y$:
$$y = 2(3) - 3$$
Multiply first, according to order of operations:
$$y = 6 - 3$$
Subtract to solve for $y$:
$$y = 3$$
The solutions is $(3, 3)$.
