# How do you solve the system of equations 3x-3y=-9 and 3x-5y=-29 by combining the equations?

Mar 13, 2017

The easiest way to solve these equations is to subtract the two equations, this eliminating one of the variables ( $x$) and then solving for the other variable ($y$)

$x = 7 \mathmr{and} y = 10$

#### Explanation:

$+ 3 x - \left(+ 3 x\right) = 0$ so if the two equations are subtracted, the $x$ term disappears.

$\text{ } 3 x - 3 y = - 9$
$- 3 x - \left(- 5 y\right) = - \left(- 29\right) \text{ }$ This gives:

$0 x + 2 y = + 20 \text{ }$ next solve for y by dividing both sides by 2

$\frac{2 y}{2} = \frac{20}{2} \text{ }$ This gives :

$y = 10$

Next substitute $y = 10$into either of the equation and solve for $x$.

$3 x + \left(- 3\right) \times 10 = - 9$ This gives

$3 x - 30 = - 9 \text{ }$ Add 30 to both sides giving

$3 x - 30 + 30 = - 9 + 30 \text{ }$ which gives

$3 x = + 21 \text{ }$ Finally divide both sides by 3

$\frac{3 x}{3} = \frac{21}{3}$ The answer is

$x = 7$

To make sure the answer is correct, substitute the values for$x \mathmr{and} y$ into the other equation to check the answer:

$3 x - 5 y = - 29$

$3 \times 7 - 5 \times 10 = - 29 \text{ }$ this gives

$+ 21 - 50 = - 29 \text{ }$ adding the integers gives

$- 29 = - 29 \text{ }$ The answer checks.