Question

solve the system.
y + 4 = 2x
8 - 2x = y
solution:
(the solution is (2, 3))
(there is no solution)

Explanation:

Step1: Substitute \( y = 8 - 2x \) into \( y + 4 = 2x \)

Substitute the expression for \( y \) from the second equation into the first. So we get \( (8 - 2x) + 4 = 2x \).

Step2: Simplify and solve for \( x \)

Simplify the left side: \( 8 - 2x + 4 = 2x \) becomes \( 12 - 2x = 2x \). Add \( 2x \) to both sides: \( 12 = 4x \). Divide both sides by 4: \( x = 3 \).

Step3: Find \( y \) using \( y = 8 - 2x \)

Substitute \( x = 3 \) into \( y = 8 - 2x \): \( y = 8 - 2(3) = 8 - 6 = 2 \).

Answer:

The solution is \( (3, 2) \)