To find the solution to the system of equations, we need to set the two equations equal to each other since both equal y:
1. The first equation is: y = 4x + 10
2. The second equation is: y = 2x + 6
Setting them equal:
4x + 10 = 2x + 6
Now, let’s solve for x:
Subtract 2x from both sides:
4x – 2x + 10 = 6
This simplifies to:
2x + 10 = 6
Next, subtract 10 from both sides:
2x = 6 – 10
2x = -4
Now, divide both sides by 2:
x = -2
We have found x. Now let’s substitute x = -2 back into one of the original equations to find y. We’ll use the second equation:
y = 2x + 6
Substituting:
y = 2(-2) + 6
y = -4 + 6
y = 2
So the solution to the system of equations is:
(x, y) = (-2, 2)
To verify, we can plug x = -2 into the first equation:
y = 4(-2) + 10
y = -8 + 10
y = 2
Both equations give us the same result, confirming that the solution is indeed:
(-2, 2)