Solve the system of equations using elimination: minus, x, plus, 2, y, equals, minus, 2−x+2y=−2 and 6, x, minus, y, equals, minus, 4 36x−y=−43.
The given system of equations is:
1) -x + 2y = -2
2) 6x - y = -4
To solve this system using elimination, we can multiply equation 1 by 6:
6(-x + 2y) = 6(-2)
-6x + 12y = -12
Now, we can add this new equation to equation 2:
-6x + 12y + 6x - y = -12 + (-4)
11y = -16
Next, we can solve for y by dividing both sides of the equation by 11:
y = -16/11
Now that we have the value of y, we can substitute it back into one of the original equations. Let's use equation 1:
-x + 2(-16/11) = -2
-x - 32/11 = -2
To remove fractions, we can multiply both sides of the equation by 11:
-11x - 32 = -22
Now, we can solve for x by isolating the variable:
-11x = -22 + 32
-11x = 10
x = 10/(-11)
x = -10/11
Therefore, the solution to the system of equations is x = -10/11 and y = -16/11.