Systems Worksheet

The following worksheet was developed to give students practice in some of the common Algebra Two systems of equations concepts.

In the curriculum I use, Algebra Two students are introduced to determinants and Cramer's rule. I've included problems with the instruction that they should be solved using Cramer's rule. If you are not teaching Cramer, white-out those instructions, or tell your students to ignore them and solve by whatever method they choose.

I did not provide any stand-alone determinant problems, since those would be done naturally as part of the Cramer's Rule problems.

Included here are:

• Systems with two unknowns
• Systems with three unknowns
• Systems which are indeterminate
• Systems which are inconsistent
• Solving systems using Cramer's Rule (2 x 2)
• Solving word problems which are systems of 2 or 3 unknowns

Systems of Equations Worksheet

Solve the following systems of equations

1. x + 2y = 17
   x - y = -13
    
2. 3x + 2y = 14
   2x + 3y = 11
    
3. x = 5y - 10
   2x - 10y = -20
    
4. 3x - y = 20
   6x = 38 + 2y
    
5. x + y + z = 30
   x + y - z = 20
   2x + y = 35
    
6. a + b = 6
   b + c = 8
   a + c = 10
    
7. 3(a + b) - 2(a + 1) = 23
   a +3b = 2(b - a) + 21
   
   Solve using Cramer's rule
    
8. x + 4y = 11
   x - 3y = -3
    
9. 5x + 2y = 60
   4x - 3y = 25
   
   Set up a system of equations and solve the word problems
    
10. The sum of two numbers is 35. One number is 9 more than the other. What are the two numbers?
     
11. The sum of my age and my age n years ago is equal to my age in 30 years. n years ago, I was five more than half my current age. How old am I now?
     
12. Three numbers add to 25. The third number is twice the first number. The second number is one more than the first number. What are the numbers?
     
13. The cost of a car was decreased by a certain amount. The new price is 80% of the old price. If the price had been increased by the same amount instead of being decreased, the new price would have been $27,600. What was the amount of discount?

Systems of Equations Worksheet: Answer Key