# How do you solve 2X-3Y=21 and 5X+4Y=-5?

Apr 13, 2018

Apr 13, 2018

(3,-5)

#### Explanation:

I'm going to assume you are looking for the intersection of the two.
Lets start by solving both for y.
$2 X - 3 Y = 21$, therefore $3 Y = 2 X - 21$, and $Y = \frac{2 X - 21}{3}$
$5 X + 4 Y = - 5$, $4 Y = - 5 X - 5$ and $Y = - \frac{5}{4} \left(X + 5\right)$
Now lets try seeing for what value of x, these two equations are equal (and therefore Y=Y)
$Y = Y , \frac{2 X - 21}{3} = - \frac{5}{4} \left(X + 1\right)$
$4 \left(2 X - 21\right) = - 15 \left(X + 1\right)$
$4 \left(2 X - 21\right) + 15 \left(X + 1\right) = 0$
$8 X - 84 + 15 X + 15 = 0$
$23 X - 69 = 0$
And finally,
$X = 3$
Now, lets find the value of y but inserting this x into either of the original equations!
$2 X - 3 Y = 21$
$2 \left(3\right) - 3 Y = 21$
$6 - 3 Y = 21$
$3 Y = - 15$
$Y = - 5$