Solve the system of equations given by y = 2x + 3 and y = -x + 5.

• A. x = 5/3, y = 11/3
• B. x = 2/3, y = 13/3
• C. x = 1, y = 5
• D. x = 0, y = 3

Answer: (B)

Finding where the two lines meet by equating their y-values. Since both equations describe y, set 2x + 3 equal to -x + 5. Solving for x: 2x + 3 = -x + 5 leads to 3x = 2, so x = 2/3. Then find y by substituting back into either equation: y = 2x + 3 = 2*(2/3) + 3 = 4/3 + 3 = 13/3. (Checking with the other equation gives y = -x + 5 = -2/3 + 5 = 13/3 as well.) Therefore the solution is x = 2/3, y = 13/3.