# How do you solve the system of equations: 4x + 2y = 14 and 4x + 3y = 6?

Nov 6, 2016

$x = \frac{15}{2}$ and $y = - 8$

#### Explanation:

Step 1) First solve the second equation for $y$ while keeping both sides of the equation balanced:

$4 x + 2 y = 14$

$4 x + 2 y - 4 x = 14 - 4 x$

$2 y = 14 - 4 x$

$\frac{2 y}{2} = \frac{14 - 4 x}{2}$

$y = 7 - 2 x$

Step 2) Substitute $7 - 2 x$ for $y$ in the first equation and solve for $x$ while keeping both sides of the equation balanced:

4x + 3(7 - 2x) = 6#

$4 x + 21 - 2 x = 6$

$2 x + 21 = 6$

$2 x + 21 - 21 = 6 - 21$

$2 x = - 15$

$\frac{2 x}{2} = \frac{15}{2}$

$x = \frac{15}{2}$

Step 3) Substitute $\frac{15}{2}$ for $x$ in the solution for Step 1 to find $y$:

$y = 7 - 2 \left(\frac{15}{2}\right)$

$y = 7 - 15$

$y = - 8$