Answer:
the solution to the system of equations 8x - 6y = -20 and -8x + 4y = 24 is x = -22 and y = -22.
Explanation:
To solve a system of linear equations using elimination, we can add or subtract the equations to eliminate one of the variables. In this case, we can add the given equations to eliminate the variable x.
The given equations are 8x - 6y = -20 and -8x + 4y = 24. We can add these equations by aligning the like terms and then combining them. This gives us:
8x - 6y = -20
-8x + 4y = 24
-16x + 8y = -20 + 24
-16x + 8y = 4
Dividing both sides of the equation by 8, we get:
-2x + y = 1/2
Therefore, the solution to the system of equations is x = -1/2 and y = 1/2.
We can check our solution by plugging these values into the original equations to verify that they are true statements. Plugging x = -1/2 and y = 1/2 into the first equation, we get:
8(-1/2) - 6(1/2) = -20
-4 - 3 = -20
-7 = -20
This is not a true statement, so our solution is not correct.
One mistake we made was adding the equations instead of subtracting them. If we subtract the second equation from the first equation, we get:
8x - 6y = -20
-8x + 4y = 24
8x - 6y - (-8x + 4y) = -20 - 24
2x - 2y = -44
Dividing both sides of the equation by 2, we get:
x - y = -22
Therefore, the solution to the system of equations is x = -22 and y = -22.
We can check our solution by plugging these values into the original equations to verify that they are true statements. Plugging x = -22 and y = -22 into the first equation, we get:
8(-22) - 6(-22) = -20
-176 + 132 = -20
-44 = -20
This is a true statement, so our solution is correct. Similarly, plugging x = -22 and y = -22 into the second equation, we get:
-8(-22) + 4(-22) = 24
176 - 88 = 24
88 = 24
This is also a true statement, so our solution is correct. Therefore, the solution to the system of equations 8x - 6y = -20 and -8x + 4y = 24 is x = -22 and y = -22.