y = -x + 6
y = 3x - 2
To find the point of intersection between the two equations, we can set them equal to each other and solve for x and y:
-x + 6 = 3x - 2
Adding x to both sides:
6 = 4x - 2
Adding 2 to both sides:
8 = 4x
Dividing both sides by 4:
2 = x
Now, substitute this value back into one of the original equations to solve for y:
y = 3(2) - 2
y = 6 - 2
y = 4
Therefore, the point of intersection is (2, 4).
To find the solution to the system of equations, let's use the method of substitution.
First, let's solve one of the equations for one variable in terms of the other variable. Let's solve the second equation, y = 3x - 2, for y.
Rearranging the equation:
y = 3x - 2
Now, substitute this expression for y into the first equation, y = -x + 6.
Replace y with 3x - 2:
3x - 2 = -x + 6
Next, let's solve this equation for x.
Combine like terms:
3x + x = 6 + 2
4x = 8
To isolate x, divide both sides of the equation by 4:
4x/4 = 8/4
x = 2
Now that x = 2, substitute this value back into either of the original equations. Let's use the first equation, y = -x + 6.
Replace x with 2:
y = -(2) + 6
y = -2 + 6
y = 4
So, the solution to the system of equations is x = 2 and y = 4.