Question

Does anyone know how to solve this math equation?
(Solve by Elimination, Substitution, or Matrices)
Thank you !!!

Answer 1

Answer:

x = 8; y = -6

Step-by-step explanation:

We have a system of equations.

$\dfrac{3(x - 2)}{2} - \dfrac{y - 2}{4} = 11$

$\dfrac{2(x + 2)}{5} - \dfrac{y}{3} = 6$

First, let's multiply both sides of each equation by the LCM of both denominators of that equation to eliminate all denominators.

First equation:

$8 \times \dfrac{3(x - 2)}{2} - 8 \times \dfrac{y - 2}{4} = 8 \times 11$

$12(x - 2) - 2(y - 2) = 88$

$12x - 24 - 2y + 4 = 88$

$12x - 2y = 108$

$6x - y = 54$

The equation above is the simplified first equation.

Second equation:

$\dfrac{2(x + 2)}{5} - \dfrac{y}{3} = 6$

$15 \times \dfrac{2(x + 2)}{5} - 15 \times \dfrac{y}{3} = 15 \times 6$

$6(x + 2) - 5y = 90$

$6x + 12 - 5y = 90$

$6x - 5y = 78$

The equation above is the simplified second equation.

The simplified system of equations is:

$6x - y = 54$

$6x - 5y = 78$

The x term of both equations is 6x. If we multiply both sides of the second equation by -1 to get a first term of -6x, then when it is added to 6x, the x terms are eliminated.

Now we rewrite the first simplified equation as it is. Below it, we write the second equation multiplied by -1 on both sides. Then we add the equations.

$6x - y = 54$

$-6x + 5y = -78$

Add the equations to get:

$4y = -24$

$y = -6$

Now we substitute -6 for y in the first simplified equation and solve for x.

$6x - y = 54$

$6x - (-6) = 54$

$6x + 6 = 54$

$6x = 48$

$x = 8$

Solution: x = 8; y = -6