How do you solve the system of equations 5x + y = 11 and - 3x - 7y = - 13?

Mar 24, 2017

$x = 2$

$y = 1$

Explanation:

The plan is to eliminate either one of the variables; $y$ seems easier.

Eqn 1: $\text{ } 5 x + y = 11$

Eqn 2: $\text{ } - 3 x - 7 y = - 13$

Multiply eqn 1 by $7$ to make it eqn 3:

$35 x + 7 y = 77$

Add eqn 3 + eqn 2:

$32 x = 64$

Dividing both sides by $32$, we get

$x = 2$

Substitute $x = 2$ into any of the equations, let's say eqn 1 in this case

$5 \cdot \left(2\right) + y = 11$

$10 + y = 11$

$y = 1$