To solve this system of equations, we are going to use the substitution method. Substitution the equation where the variable is isolated into the second equation. In this system of equations, y is isolated, so we will replace y in the second equation with 3x + 1.
2x + 3y = 14 2x + 3(3x + 1) = 14 2x + 9x + 3 = 14 We will add the like terms and subtract 3 from both sides of the equation. 11x + 3 = 14 11x = 11 x = 1 In this system of equations, x is equal to 1. Now we will go back and solve for y, plugging in 1 for x. 3(1) + 1 = y 2(1) + 3y = 14
3 + 1 = y 2 + 3y = 14
4 = y 3y = 2
4 = y 4 = y
The solution to this system of equations is (1, 4).
