# How do you solve the system x+2y=5 and 2x-3y=-4 by substitution?

Feb 10, 2016

Solution is $x = 1$ and $y = 2$.

#### Explanation:

In substitution method, we have to take the value of one variable (in terms of another variable), from one equation and then put it in second equation. In the given example, first equation gives us

$x = 5 - 2 y$ and substituting it in second we get

$2 \left(5 - 2 y\right) - 3 y = - 4$ or

$10 - 4 y - 3 y = - 4$ or $10 - 7 y = - 4$

Moving similar terms on one side gives us

$- 7 y = 4 + 10 = 14$ i.e. $y = 2$

Putting this equation back in first, we get $x$ as follows

$x = 5 - 2 \cdot 2$ or $x = 5 - 4$ or $x = 1$

Hence solution is $x = 1$ and $y = 2$.