# How do you solve 3x -4y = 23 and 5x +2y = 21?

Jun 21, 2016

$x = 5$ and $y = - 2$

#### Explanation:

The two equations are $3 x - 4 y = 23$ ......(A) and

$5 x + 2 y = 21$ ......(B)

As is apparent we can eliminate $y$ by multiplying equation (B) by $2$ and adding it to (A). We now get

$2 \times \left(5 x + 2 y\right) + 3 x - 4 y = 2 \times 21 + 23$ or

$10 x + 4 y + 3 x - 4 y = 42 + 23$ or $13 x = 65$ i.e. $x = \frac{65}{13} = 5$

Now putting this value of $x$ in (B), we get

$5 \times 5 + 2 y = 21$ or $25 + 2 y = 21$

Hence $y = 21 - 25 = - 4$ or $y = - 2$