What value of y makes the following system of equations true?
3x + 6y=12
5x + 6y = 4
If you subtract the second equation from the first, you get:
-2x = 8
x = -4
Substitute that into either equation to find the value of y.
To find the value of y that makes the system of equations true, we need to solve for y using the given equations.
First, let's eliminate the x variable by subtracting the second equation from the first equation:
(3x + 6y) - (5x + 6y) = 12 - 4
This simplifies to:
-2x = 8
Now, we can solve for x by dividing both sides of the equation by -2:
x = -4
Next, we substitute this value of x into one of the original equations. Let's use the first equation:
3x + 6y = 12
Substituting x = -4:
3(-4) + 6y = 12
Simplifying further:
-12 + 6y = 12
Add 12 to both sides:
6y = 24
Now, divide both sides of the equation by 6 to solve for y:
y = 4
Thus, the value of y that makes the system of equations true is y = 4.