# How do you solve the system of equations: 4x+3y=7 and -2x+y=9?

Aug 8, 2015

The solution for the system of equations is:
color(blue)(x=-2, y=5

#### Explanation:

$\textcolor{b l u e}{4 x} + 3 y = 7$............equation $\left(1\right)$

$- 2 x + y = 9$, multiplying this equation by $2$
$\textcolor{b l u e}{- 4 x} + 2 y = 18$......equation $\left(2\right)$

Now, we can solve the system of equations through elimination.
Adding the two equations eliminates color(blue)(4x

$\cancel{\textcolor{b l u e}{4 x}} + 3 y = 7$
$\cancel{\textcolor{b l u e}{- 4 x}} + 2 y = 18$

$5 y = 25$

color(blue)(y=5

Now, we find $x$ by substituting the value of $y$ in equation $1$:

$4 x + 3 y = 7$

$4 x = 7 - 3 y$

$x = \frac{7 - 3 y}{4}$

$x = \frac{\left(7 - 3 \cdot 5\right)}{4}$

$x = \frac{\left(7 - 15\right)}{4}$

$x = - \frac{8}{4}$

color(blue)(x=-2