# How do you solve 5x - 2y = 10 and 3x + 2y = 6 using substitution?

May 25, 2018

$x = 2 \mathmr{and} y = 0$

#### Explanation:

I wonder why you would want to solve this by substitution when elimination is an easier and more obvious method because of the $- 2 y \mathmr{and} + 2 y$ terms.?

Make a single variable the subject:
$3 x + 2 y = 6 \text{ "rarr 2y = 6-3x" } \rightarrow \textcolor{b l u e}{y = 3 - \frac{3 x}{2}}$

Substitute this expression for $y$ in the first equation:

$5 x - 2 \textcolor{b l u e}{y} = 10$

$5 x - 2 \left(\textcolor{b l u e}{3 - \frac{3 x}{2}}\right) = 10$

$5 x - 6 + 3 x = 10$

$8 x = 16$

$x = 2$

color(blue)(y = 3-(3(2))/2

$y = 0$

Compare the Elimination method

$\text{ "5x-2y=10" } \ldots . A$
$\text{ "ul(3x+2y =6)" } \ldots . . B$
$\text{ "8x " "=16" } \leftarrow A + B$
$\textcolor{w h i t e}{\times \times x . x} x = 2$

Substitute in $B$

$3 x + 2 y = 6$
$3 \left(2\right) + 2 y = 6$
$\cancel{6} + 2 y = \cancel{6}$
$y = 0$