Solve a system by substitution

Answer Key - Grade 8 Math Worksheet - Challenge Me

Circle the best answer, or write your answer on the line.

1. 1.

   Pia solves 2x + y = 5 and 5x + 2y = 9 by substitution. Neither equation starts with y alone. What is the solution (x, y)?

   (-1, 7)
2. 2.

   Ren's puzzle card shows -2x + y = 3 and 5x - 2y = -4, with a doodle of a very calm cat. What is the solution (x, y)?

   (2, 7)
3. 3.

   Esme solves the system x + y = 6 and 4x - 2y = 12 by substitution. What is the solution (x, y)?

   (4, 2)
4. 4.

   Noah's system is x = 2y + 1 and -2x + 5y = 0. The first rule tells what x is. What is the solution (x, y)?

   (5, 2)
5. 5.

   Milo solves x = 3y + 1 and -2x + 3y = -5 by putting the rule for x into the other equation. What is the solution (x, y)?

   (4, 1)
6. 6.

   Luz meets a system with x alone: x = -2y + 4 and 4x + 5y = 7. What is the solution (x, y)?

   (-2, 3)
7. 7.

   Ari unwinds two kite strings, blue (x m) and red (y m): y = 2x + 4 and x + y = 64. What point (blue m, red m) solves the system?

   (20, 44)
8. 8.

   Bo reads a short book (x pages) and a long one (y pages), with snacks: y = 3x + 20 and x + y = 240. What point (short, long) solves the system?

   (55, 185)
9. 9.

   Jun solves 2x + y = 5 and 6x + 3y = 9 by getting y alone first. How many solutions does the system have?

   • exactly one solution
   • infinitely many solutions
   • no solution
10. 10.

    Noah finds -4x + y = -2 and x + 2y = -4 on the back of a worksheet (a mystery bonus). How many solutions does the system have?

    • exactly one solution
    • infinitely many solutions
    • no solution