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

Jul 30, 2016

$x = \frac{3}{5}$
$y = \frac{19}{5}$

#### Explanation:

$2 x + y = 5$
Putting $y = 3 x + 2$ in the above equation we get
$2 x + 3 x + 2 = 5$
or
$5 x + 2 = 5$
or
$5 x = 5 - 2$
or
$5 x = 3$
or
$x = \frac{3}{5}$=======Ans $1$
By putting $x = \frac{3}{5}$ in the equation $y = 3 x + 2$
we get
$y = 3 \left(\frac{3}{5}\right) + 2$
or
$y = \frac{9}{5} + 2$
or
$y = \frac{9 + 2 \left(5\right)}{5}$
or
$y = \frac{9 + 10}{5}$
or
$y = \frac{19}{5}$=====Ans $2$

Jul 30, 2016

$x = \frac{3}{5} , y = 3 \frac{4}{5}$

#### Explanation:

This type of question is particularly common when working with straight lines.

Note that there is a single $y$ term in both equations.

$y = - 2 x + 5 \text{ and } y = 3 x + 2$

At the point where the two lines intersect, the $x - \mathmr{and} y -$ values are equal.

If $\text{ y = y" }$ it follows that:

$3 x + 2 = - 2 x + 5$

$5 x = 3$

$x = \frac{3}{5}$

There are now two equations to find a value for y. If we get the same answer for each we will know our answers are correct.

$y = 3 \times \frac{3}{5} + 2 = 3 \frac{4}{5} \text{ } y = - 2 \times \frac{3}{5} + 5 = 3 \frac{4}{5}$