# How do you solve the system 5x – 3y = 13 and 4x – 3y = 11?

May 21, 2018

$x = 2$ and $y = - 1$

#### Explanation:

After subtracting second equation from first one,

$\left(5 x - 3 y\right) - \left(4 x - 3 y\right) = 13 - 11$

$x = 2$

Hence,

$5 \cdot 2 - 3 y = 13$

$10 - 3 y = 13$

$- 3 y = 3$, thus $y = \frac{3}{- 3} = - 1$

May 21, 2018

$\left(2 , - 1\right)$

#### Explanation:

Solving by Elimination

Multiply the first equation by $- 1$ to temporarily eliminate $y$. Then add to the second equation (unmodified).

$- \left(5 x - 3 y = 13\right)$
$- 5 x + 3 y = - 13$
$4 x - 3 y = 11$

$- x = - 2$
$x = 2$

Substitute into either equations to solve for $y$
$5 \left(2\right) - 3 y = 13$
$10 - 3 y = 13$
$- 3 y = 3$
$y = - 1$

Answer: $\left(2 , - 1\right)$