Systems of equations word problems, step by step
A system of equations is easiest to see as a scene: two things you do not know, and two facts that pin them down.
The question
Find the price of one muffin and one peach.
Together, 1 muffin and 1 peach cost $11. On a second visit, 5 muffins and 1 peach together cost $27.
a muffin costs $4, a peach costs $7
1 × 4 + 1 × 7 = 11
asked:Find the price of one muffin and one peach.
a muffin costs $4, a peach costs $7
- Read it through. There are TWO prices to find — one for each item. The two baskets give you two facts, and together they pin both prices down.
- Find the two prices that make BOTH baskets come out right: a muffin costs $4, a peach costs $7.
- Check against a basket you were given: 1 × 4 + 1 × 7 = 11. It matches, so the prices are right.
- Answer what was asked — "Find the price of one muffin and one peach.": a muffin costs $4, a peach costs $7.
How it works.
- 01
Read it through. There are TWO prices to find — one for each item. The two baskets give you two facts, and together they pin both prices down.
- 02
Find the two prices that make BOTH baskets come out right: a muffin costs $4, a peach costs $7.
- 03
Check against a basket you were given: 1 × 4 + 1 × 7 = 11. It matches, so the prices are right.
- 04
Answer what was asked — "Find the price of one muffin and one peach.": a muffin costs $4, a peach costs $7.