6x-y=-4
2x+2y=15
Solve for y
Multiply top equation by 2.
12x-2y = -8
2x+2y=15
Add the two equations.
14x = 7
Solve for x, then insert value into one equation to find y. Check by inserting value of x into the other equation.
To solve for y, we can use the method of substitution or elimination. In this case, let's use the method of elimination.
Given the system of equations:
6x - y = -4 (Equation 1)
2x + 2y = 15 (Equation 2)
We'll multiply Equation 1 by 2 to match the coefficients of y:
2(6x - y) = 2(-4)
12x - 2y = -8 (Equation 3)
Now, we'll add Equation 2 and Equation 3 together:
(12x - 2y) + (2x + 2y) = -8 + 15
Simplifying the equation further:
12x - 2y + 2x + 2y = 7
14x = 7
Dividing both sides of the equation by 14 to solve for x:
x = 7/14
x = 1/2
Now that we have the value of x, we can substitute it back into either Equation 1 or Equation 2 to find the value of y. Let's substitute it into Equation 1:
6(1/2) - y = -4
3 - y = -4
To isolate y, let's subtract 3 from both sides of the equation:
-y = -4 - 3
-y = -7
Finally, to solve for y, let's multiply both sides of the equation by -1 to get:
y = 7
So, the solution to the system of equations is x = 1/2 and y = 7.