To solve the system of equations given by y = 2x + 4 and 2y = 6x + 12, we can follow several steps to find the values of x and y.
Step 1: Substitute
We start with the first equation: y = 2x + 4. We can substitute this expression for y into the second equation.
Step 2: Substitute into the second equation
The second equation is:
2y = 6x + 12
By substituting y in this equation:
- 2(2x + 4) = 6x + 12
Step 3: Simplify
Next, we will simplify this equation:
- 4x + 8 = 6x + 12
Step 4: Rearrange the equation
Now, let’s rearrange the terms to isolate x:
- 4x + 8 – 6x = 12
- -2x + 8 = 12
- -2x = 12 – 8
- -2x = 4
- x = -2
Step 5: Substitute back to find y
Now that we have x, we can find y using the first equation:
- y = 2(-2) + 4
- y = -4 + 4
- y = 0
Conclusion:
The solution to the system of equations is (x, y) = (-2, 0). This means the two lines represented by the equations intersect at the point (-2, 0).