To solve the system of equations, we start with the two equations:
- 1. y = x + 2
- 2. y = 2x + 7
Since both equations are equal to y, we can set them equal to each other:
x + 2 = 2x + 7
Now, we will solve for x. First, we can rearrange the equation by getting all terms involving x on one side and constant terms on the other:
x – 2x = 7 – 2
This simplifies to:
-x = 5
Next, we can multiply both sides by -1 to solve for x:
x = -5
Now that we have the value of x, we can substitute it back into one of the original equations to find the corresponding value of y. Let’s use the first equation:
y = x + 2
Substituting x = -5, we get:
y = -5 + 2
This simplifies to:
y = -3
So, the solution to the system of equations is x = -5 and y = -3. The ordered pair (-5, -3) represents the point where the two lines intersect.