# Question #1622e

Feb 14, 2018

$x = 7$ and $y = 6$

If you like point form, it is: $\left(7 , 6\right)$

#### Explanation:

Given:

$2 x + y = 20 \text{ [1]}$
$6 x - 5 y = 12 \text{ [2]}$

We can use equation [1] to write y in terms of x by subtracting 2x from both sides:

$y = 20 - 2 x \text{ [1.1]}$
$6 x - 5 y = 12 \text{ [2]}$

Substitute the right side of equation [1.1] for y in equation [2]:

$6 x - 5 \left(20 - 2 x\right) = 12 \text{ [2.1]}$

Solve for the value of x:

$6 x - 100 + 10 x = 12 \text{ [2.1]}$

$16 x = 112$

$x = 7$

We can use either equation [1] or [2] to find the corresponding value of y; I shall use equation [1]:

$2 \left(7\right) + y = 20$

$y = 6$

Verify that the point $\left(7 , 6\right)$ satisfies both equations:

$2 \left(7\right) + 6 = 20$
$6 \left(7\right) - 5 \left(6\right) = 12$

$20 = 20$
$12 = 12$

Verified