To find the solution to the system of equations given by y = 5x + 6 and y = 3x + 4, we need to set the two equations equal to each other since they both equal y:
5x + 6 = 3x + 4
Now, we will solve for x. First, let’s get all the x terms on one side:
5x – 3x = 4 – 6
This simplifies to:
2x = -2
Dividing both sides by 2 gives us:
x = -1
Now that we have the value of x, we can substitute it back into either of the original equations to find the corresponding y value. Let’s use the first equation:
y = 5(-1) + 6
This simplifies to:
y = -5 + 6 = 1
So, the solution to the system of equations is:
(x, y) = (-1, 1)
This means the two lines intersect at the point (-1, 1).