# How do you solve 4x + 2y = 10 and x - y = 13 using substitution?

Mar 7, 2016

$x = 6$ and $y = - 7$

#### Explanation:

We can solve $4 x + 2 y = 10$ and x−y=13 by substituting the value of one variable in terms of another variable from one equation and putting this value in other equation. This will give us value of 'another' variable, which when put in either should give us other variable.

In the given problem, let us get rge value of $x$ in the equation x−y=13. This gives us $x = y + 13$. Now putting this value of $x$ in $4 x + 2 y = 10$, we get

$4 \left(y + 13\right) + 2 y = 10$ or $4 y + 52 + 2 y = 10$ and on transposition of like terms, we get

$6 y = 10 - 52 = - 42$ i.e. $y = - 7$ and $x = - 7 + 13 = 6$

Hence, $x = 6$ and $y = - 7$