# What is the value of x+y for the equation? y=4x-5, and y=-4x+19

Apr 28, 2018

$x + y = 10$

#### Explanation:

$y = 4 x - 5$
$y = - 4 x + 19$

From this we can say

$4 x - 5 = y = - 4 x + 19$

$4 x - 5 = - 4 x + 19$

Now add $5$ to both sides of the equation:

$4 x - 5 \setminus \underline{+ 5} = - 4 x + 19 \setminus \underline{+ 5}$

$4 x = - 4 x + 24$

Then add $4 x$ to both sides of the equation:

$4 x \setminus \underline{+ 4 x} = - 4 x \setminus \underline{+ 4 x} + 24$

$8 x = 24$

Now we can divide both sides of the equation by $8$, or you can say, that

$8 x = 24$

so

$x = \frac{24}{8} = 3$

Knowing the value of $x$, we can easily find the value of $y$.

$y = 4 x - 5$

$4 x - 5 = 4 \cdot 3 - 5 = 12 - 5 = 7$

So

$x = 3 \mathmr{and} y = 7$

Therefore

$x + y = 3 + 7 = 10$