Question

solve the following system of equations by substitution:
y = 3x - 2
x - y = -2
write the solution as an ordered pair.

Explanation:

Step1: Identify substitution

We have \( y = 3x - 2 \) and \( x - y = -2 \). Substitute \( y = 3x - 2 \) into the second equation.
So, \( x - (3x - 2) = -2 \).

Step2: Simplify the equation

Simplify \( x - 3x + 2 = -2 \). Combine like terms: \( -2x + 2 = -2 \).

Step3: Solve for x

Subtract 2 from both sides: \( -2x = -4 \). Divide by -2: \( x = 2 \).

Step4: Solve for y

Substitute \( x = 2 \) into \( y = 3x - 2 \). So, \( y = 3(2) - 2 = 6 - 2 = 4 \).

Answer:

\((2, 4)\)