# How do you solve 2x + 3y = -6 and 3x + 2y = 25?

Aug 15, 2015

$\textcolor{red}{\text{The solution is (5,-3).}}$

One way is to use the method of elimination.

Step 1. Enter the equations.

[1] $3 x + 7 y = - 6$
[2] $x - 2 y = 11$

Step 2. Multiply each equation by a number to get the lowest common multiple of the coefficients of one variable.

Multiply Equation 2 by $3$.

[3] $3 x - 6 y = 33$

Step 3. Subtract Equation 3 from Equation 1.

$3 x + 7 y = \textcolor{w h i t e}{1} - 6$
$3 x - 6 y = \text{ } 33$
stackrel(——————————)(" "color(white)(1)13y=-39)

[4] $y = - 3$

Step 4. Substitute Equation 4 in Equation 1.

$3 x + 7 y = - 6$
$3 x + 7 \left(- 3\right) = - 6$
$3 x - 21 = - 6$
$3 x = 15$

$x = 5$

Solution: The solution that satisfies both equations is $\left(5 , - 3\right)$.

Check: Substitute the values of $x$ and $y$ in Equation 2.

$x - 2 y = 11$
$5 - 2 \left(- 3\right) = 11$
$5 + 6 = 11$
$11 = 11$

It checks!

Our solution is correct.