math class 678 4-in-1 skill sheets
8.EE.C.8c 8th Grade Expressions & Equations

Systems Word Problems

Solve real-world and mathematical problems leading to two linear equations in two variables.

How to explain it

At this standard, students solve word problems involving two unknowns by defining variables, writing a system of two equations, solving by substitution or elimination, and interpreting the answer in context.

The anchor students hold onto: Step 1: Define variables. Step 2: Write two equations (one per constraint). Step 3: Solve. Step 4: Interpret the answer in context.

Systems word problems appear throughout algebra and standardized tests. Students apply this skill in Algebra 1, chemistry (mixture/dilution), and economics contexts.

Worked examples

Example 1 Sum & Difference
Sum is 20; diff is 6.
Step 1Let x = larger, y = smaller.
Step 2x + y = 20 ; x − y = 6.
Step 3Add: 2x = 26 → x = 13.
Step 4y = 20 − 13 = 7.
Answer13 and 7
Example 2 Price Problem
Total $13; juice $3 more.
Step 1Let j = juice, w = water.
Step 2j + w = 13 ; j = w + 3.
Step 3Sub: (w + 3) + w = 13 → w = 5.
Step 4j = 5 + 3 = 8. Juice $8, water $5.
Answerjuice $8, water $5
Example 3 Mixture Problem
10% and 40% make 25%, 60 mL.
Step 1Let x = 10%, y = 40% solution.
Step 2x + y = 60 ; 0.10x + 0.40y = 15.
Step 3Sub x = 60−y: 6 + 0.30y = 15.
Step 40.30y = 9 → y = 30, x = 30.
Answer30 mL each

Common mistakes

What students write Writing only one equation from the word problem instead of two separate constraints.
The fix Identify every condition stated in the problem — each independent condition becomes its own equation.
What students write Stopping at the ordered-pair solution without connecting it to the problem context.
The fix Write a complete sentence using the variable definitions to interpret each value after solving.

Teacher tip

Head off the two predictable errors before they happen. First: Identify every condition stated in the problem — each independent condition becomes its own equation. Second: Write a complete sentence using the variable definitions to interpret each value after solving.