# How do you solve this system of equations: 2x + 4y = 9; 5x - y = - \frac { 21} { 2}?

Jan 31, 2018

$\left(x , y\right) \to \left(- \frac{3}{2} , 3\right)$

#### Explanation:

$2 x + 4 y = 9 \to \left(1\right)$

$5 x - y = - \frac{21}{2} \to \left(2\right)$

$\text{multiply equation "(2)" by 4}$

$\text{this will make the coefficients of y opposites so we can}$
$\text{add the equations and eliminate the y term}$

$\Rightarrow 20 x - 4 y = - 42 \to \left(3\right)$

$\text{add equations "(1)" and "(3)" term by term to eliminate y}$

$\left(2 x + 20 x\right) + \left({\cancel{4 y - 4 y}}^{0}\right) = \left(9 - 42\right)$

$\Rightarrow 22 x = - 33$

$\text{divide both sides by 22}$

$\frac{\cancel{22} x}{\cancel{22}} = \frac{- 33}{22}$

$\Rightarrow x = - \frac{3}{2}$

$\text{substitute "x=-3/2" in equation "(1)" and solve for y}$

$- 3 + 4 y = 9$

$\text{add 3 to both sides}$

$\cancel{- 3} \cancel{+ 3} + 4 y = 9 + 3$

$\Rightarrow 4 y = 12$

$\text{divide both sides by 4}$

$\frac{\cancel{4} y}{\cancel{4}} = \frac{12}{4}$

$\Rightarrow y = 3$

$\text{the point of intersection is } \left(- \frac{3}{2} , 3\right)$
graph{(y+1/2x-9/4)(y-5x-21/2)((x+3/2)^2+(y-3)^2-0.04)=0 [-10, 10, -5, 5]}