GED Math Review: Solving Systems by Substitution

Questions:

A. Solve each system by substitution. Check your answer.

1. x + y = 3
   2x + 4y = 8
   
   Solution: __________
2. x + 2y = 7
   4x + 3y = 3
   
   Solution: __________
3. -4x + y = 3
   5x - 2y = -9
   
   Solution: __________
4. 8x - 7y = -2
   -2x - 3y = 10
   
   Solution: __________
5. 2x - 2y = 5
   4x - 4y = 9
   
   Solution: __________
6. 2x + 7y = 2
   4x + 2y = -2
   
   Solution: __________
7. 2x - y = 7
   2x + 7y = 31
   
   Solution: __________
8. x - 2y = -4
   4y = 2x + 8
   
   Solution: __________
   
   B. Tell whether it is more efficient to solve for x and then substitute for x or to solve for y and then substitute for y. Explain your reasoning. Then solve the system.
9. 9x - 3y = 15
   x + 3y = -8
   
   ______________________________________
   ______________________________________
   Solution: __________
10. x/2 + y = 6
    x/4 + y/2 = 3
    
    ______________________________________
    ______________________________________
    Solution: __________

Answers:

1. (2, 1)
2. (-3, 5)
3. (1, 7)
4. (-2, -2)
5. no solution
6. (-3/4, 1/2)
7. (5, 3)
8. infinitely many solutions
9. (1, -3)
10. infinitely many solutions

Reference:

Complete Test Preparation for the GED Test 2014 by Steck-Vaughn