# How do you solve 3x – 2y = 26 and -7x + 3y = -49 using substitution?

Apr 15, 2018

$x = 4$
$y = - 7$

#### Explanation:

Solve by simultaneous equations:

$3 x - 2 y = 26$
$- 7 x + 3 y = - 49$

Rearrange $3 x - 2 y = 26$ to make $x$ the subject of the equation:

$3 x = 26 + 2 y$
$x = \frac{26 + 2 y}{3}$

Substitute the value of $x$ into $- 7 x + 3 y = - 49$:
$- 7 \cdot \left(\frac{26 + 2 y}{3}\right) + 3 y = - 49$
$- 7 \cdot \left(\frac{26}{3} + \frac{2 y}{3}\right) + 3 y = - 49$

Multiply out the brackets:
$- \frac{182}{3} + - \frac{14 y}{3} + 3 y = - 49$

Rearrange and place like terms together:
$- \frac{14 y}{3} + 3 y = - 49 + \frac{182}{3}$

Simplify and solve for y:

$- \frac{5 y}{3} = \frac{35}{3}$
$- 5 y = \frac{35}{3} \cdot 3$
$- 5 y = 35$
$y = \frac{35}{-} 5$
$y = - 7$

Use value of y to subsitute into any of the two original equations and solve for x:

$3 x - 2 y = 26$
$3 x - 2 \cdot \left(- 7\right) = 26$
$3 x + 14 = 26$
$3 x = 26 - 14$
$3 x = 12$
$x = \frac{12}{3}$
$x = 4$