# How do you solve y = 3x + 5 and y = 2x + 4?

In order to eliminate one of the variables, say x, transform the equation (2) $y = 2 x + 4$, by multiplying both sides by 3/2. The result is (2') $\frac{3}{2} y = 3 x + 6$. Now, subtract equation (1), namely $y = 3 x + 5$, from equation (2'), and one gets $\frac{1}{2} y = 1$.So, y = 2. Substituting 2 for y in equation (1) one gets $2 = 3 x + 5$, and by subtracting 5 from both sides, one gets $- 3 = 3 x$. So, x = -1.