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drek231 [11]
3 years ago
10

Does anyone know how to solve this math equation?

Mathematics
1 answer:
garik1379 [7]3 years ago
6 0

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

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