Question

Solve the following system of equations

1/2x+1/4y=-2
-2/3x+1/2y=6

x=

y=​

Answer 1

y = 4

x = -6

Explanation:

1/2 x + 1/4 y= -2 first equation

-2/3 x + 1/2 y = 6 second equation

solution:

from the first equation:

8(1/2 x + 1/4 y) = -2*8

8x*1/2 + 8y*1/4 = -16

8x/2 + 8y/4 = -16

4x + 2y = -16 third equation

from the second equation

6(-2/3 x + 1/2 y) = 6*6

6x*-2/3 + 6y*1/2 = 36

-12x/3 + 6y/2 = 36

-4x + 3y = 36 fourth equation

from the third & fourth equation:

4x + 2y = -16

-4x + 3y = 36

0 + 5y = 20

5y = 20

y = 20/5

y = 4

from the fourth equation:

-4x + 3y = 36

-4x + 3*4 = 36

-4x + 12 = 36

-4x = 36 - 12

-4x = 24

x = 24/-4

x = -6

Check:

from the first equation:

1/2 x + 1/4 y = -2

1/2 *-6 + 1/4 * 4 = -2

-3 + 1 0 -2

from the second equation:

-2/3 x + 1/2 y = 6

-2/3 * -6 + 1/2 * 4 = 6

4 + 2 = 6

Answer 2

x = -6

y = 4

Explanation:

Rewriting the equations :

1. 2x + y = -8
2. 4x - 3y = -36

Now, solving the two equations using substitution method, we get :

x = -6

y = 4