## Introductory Algebra for College Students (7th Edition)

The solution to this system of equations is $(3, -1)$.
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 $(3, -1)$.