To find the solution of the system of equations, we can set the two equations equal to each other since both of them equal y:
1. Start with the equations:
- y = 4x + 10
- y = 2x + 6
2. Set them equal to each other:
4x + 10 = 2x + 6
3. Now, we’ll solve for x. First, subtract 2x from both sides:
4x – 2x + 10 = 6
2x + 10 = 6
4. Next, subtract 10 from both sides:
2x = 6 – 10
2x = -4
5. Now, divide by 2:
x = -2
Now that we have the value of x, we can substitute it back into either of the original equations to find y. Let’s use the second equation:
y = 2(-2) + 6 = -4 + 6 = 2
So, the solution to the system of equations is:
x = -2 and y = 2.
In conclusion, the intersection point of the two lines represented by the equations is (-2, 2).