# How do you solve this system of equations: 3x + 5y = 19 and 4x - y = 10?

Nov 28, 2017

$x = 3 \mathmr{and} y = 2$

#### Explanation:

I will solve your system by substitution (you can also solve this system by elimination).

4x−y=10
$3 x + 5 y = 19$

Step: Solve 4x−y=10 for $y$:

4x−y+−4x=10+−4x" " (add $- 4 x$ to both sides)

−y=−4x+10

Divide by $- 1$

y=4x−10

Step: Substitute 4x−10 for $y$ in $3 x + 5 y = 19$:

$3 x + 5 y = 19$

3x+5 (4x−10)=19

23x−50=19 " "(simplify both sides of the equation)

23x−50+50=19+50 " "(add $50$ to both sides)

$23 x = 69$

Divide both sides by $23$

$x = 3$

Step: Substitute $3$ for $x$ in y=4x−10:

y=4x−10

y=(4)(3)−10

$y = 2 \text{ }$ (simplify both sides of the equation)