To find the solution to the system of equations, we need to set the two equations equal to each other since both are equal to y:
Equation 1: y = 3x + 8
Equation 2: y = 5x + 2
Setting the equations equal gives us:
3x + 8 = 5x + 2
Now, we can solve for x. First, we’ll rearrange the equation:
8 – 2 = 5x – 3x
6 = 2x
x = 3
Now that we have the value of x, we can substitute it back into either of the original equations to find y. We’ll use the first equation:
y = 3(3) + 8
y = 9 + 8
y = 17
So the solution to the system of equations is x = 3 and y = 17. In coordinate form, the solution can be expressed as (3, 17).