Solve each system.
y=2x+2 y=-2x-6
Since both right sides are equal to y, we can say:
2x+2 = -2x-6
4x = -8
x = -2
back into y = 2x+2
y = 2(-2) + 2
= -2
x = -2, y = -2
To solve this system of equations, we can use the method of substitution. We'll solve one equation for one variable and substitute that expression into the other equation.
First, let's solve the second equation for y in terms of x:
y = -2x - 6
Next, substitute the expression for y in the first equation:
2x + 2 = -2x - 6
Now, let's isolate x by moving all the terms with x to one side:
2x + 2x = -6 - 2
4x = -8
Dividing both sides of the equation by 4:
x = -8/4
x = -2
Now that we know the value of x, we can substitute it back into one of the original equations to find y. Let's use the first equation:
y = 2x + 2
y = 2(-2) + 2
y = -4 + 2
y = -2
Therefore, the solution to the system of equations is x = -2, y = -2.