Question

what is the solution to the system of equations?
y = -2x + 6
y = 3x + 1
a. (4, 1)
b. (4, -1)
c. (-1, 4)
d. (1, 4)

Explanation:

Step1: Set the equations equal

Since the solution to the system is where the two lines intersect, we set \(3x + 1=-2x + 6\).

Step2: Solve for x

Add \(2x\) to both sides: \(3x+2x + 1=-2x+2x + 6\) → \(5x + 1 = 6\).
Subtract 1 from both sides: \(5x + 1-1 = 6-1\) → \(5x = 5\).
Divide by 5: \(x=\frac{5}{5}=1\).

Step3: Find y

Substitute \(x = 1\) into \(y = 3x + 1\): \(y=3(1)+1=4\).

Answer:

D. (1, 4)