# How do you solve the simultaneous equations 4x + 3y = 9 and 3x - y = 10?

Aug 3, 2015

$\textcolor{red}{x = 3 , y = - 1}$

#### Explanation:

One way is to use the method of elimination.

Step 1. Enter the equations.

[1] $4 x + 3 y = 9$
[2] $3 x - y = 10$

Step 2. Prepare the equations.

Multiply each equation by numbers that give one variable the same coefficient in each equation.

Multiply Equation 2 by $3$.

[3] $9 x - 3 y = 30$

Step 2. Add Equations 1 and 3.

$13 x = 39$

[3] $x = 3$

Step 3. Substitute Equation 3 in Equation 2.

$3 x - y = 10$
$3 \left(3\right) - y = 10$
$9 - y = 10$

$y = - 1$

Solution: $x = 3 , y = - 1$

Check: Substitute the values of $x$ and $y$ in Equation 1.

$4 x + 3 y = 9$
$4 \left(3\right) + 3 \left(- 1\right) = 9$
$12 - 3 = 9$
$9 = 9$

It checks!