# Question #9fb91

$x = 10$
$y = 2$

#### Explanation:

the given system of equations

$x = 3 y + 4 \text{ }$ first equation
$2 x - 3 y = 14 \text{ }$ second equation

Method of Substitution
Substitute the first equation into the second equation so that

$2 x - 3 y = 14 \text{ }$ second equation

becomes

$2 \left(3 y + 4\right) - 3 y = 14 \text{ }$ second equation

simplify

$6 y + 8 - 3 y = 14$

$6 y - 3 y = 14 - 8$

$3 y = 6$

$\frac{3 y}{3} = \frac{6}{3}$

$y = 2$
~~~~~~~~~~~~~~~~~~~~~~~~

Solve now for $x$ using the value of $y = 2$

$x = 3 y + 4 \text{ }$ first equation
$x = 3 \left(2\right) + 4 \text{ }$ first equation

$x = 6 + 4$

$x = 10$

~~~~~~~~~~~~~~~~~~~

checking:
$x = 3 y + 4 \text{ }$ first equation
$10 = 3 \left(2\right) + 4$
$10 = 6 + 4$
$10 = 10$

checking:
$2 x - 3 y = 14 \text{ }$ second equation
$2 \left(10\right) - 3 \left(2\right) = 14 \text{ }$ second equation

$20 - 6 = 14$
$14 = 14$

$x = 10$ and $y = 2$ are correct

God bless....I hope the explanation is useful.