Model with two equations
Define two variables, write an equation for each piece of information, then solve.
Why it works
Two clues pin both unknowns.
Linear · Apply · 5.1
System word problems.
Two-unknown word problems become a system: write one equation per fact, then solve. The solution gives both unknowns at once.
See it work.
Watch the method
System word problems
One equation per fact, then solve the system.
1
The system
Two lines — the solution is the point on both.
2
Find where the lines cross
Solve for x, then back-substitute for y.
3
The solution
Write the intersection point.
Practice until it feels automatic.
Your turn
Work it out.
Type (x, y).
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Answer:
The idea underneath.
From easy to tricky.
Solve the system: y=2x-6 and y=x-2. Give the point (x, y).
1
The system
Two lines — the solution is the point on both. y = 2x - 6;\; y = x - 2
2
Find where the lines cross
Solve for x, then back-substitute for y. x = 4
3
The solution
Write the intersection point. (4, 2)
Solve the system: y=2x-3 and y=-2x+13. Give the point (x, y).
1
The system
Two lines — the solution is the point on both. y = 2x - 3;\; y = -2x + 13
2
Find where the lines cross
Solve for x, then back-substitute for y. x = 4
3
The solution
Write the intersection point. (4, 5)
Solve the system: y=-x+6 and y=3x-2. Give the point (x, y).
1
The system
Two lines — the solution is the point on both. y = -x + 6;\; y = 3x - 2
2
Find where the lines cross
Solve for x, then back-substitute for y. x = 2
3
The solution
Write the intersection point. (2, 4)
Where students slip.
Trap
Writing only one equation.
Fix
Two unknowns need two equations.
Trap
Answering only one unknown.
Fix
Report both values.
Test yourself.
The Test
12 problems across three tiers. Auto-graded on submit. Hints and a full walkthrough on every question. Your work is saved on this device — sign in to keep it across devices.
0/12Answered
How to answerType just the value. Formatting won't trip you up — we ignore spaces, capital letters, commas, and subscript style, so
t₁ = 5, d = 3 and t1=5,d=3 both count. For a list of numbers, separate them with commas (e.g. 3, 10, 17).Core
Core (4)
C1
Solve the system: y=-x+1 and y=-2x+5. Give the point (x, y).
Need a hint?
- Write an equation for each fact.
- Solve the system for both unknowns.
C2
Solve the system: y=2x+5 and y=x+2. Give the point (x, y).
Need a hint?
- Write an equation for each fact.
- Solve the system for both unknowns.
C3
Solve the system: y=x+6 and y=-2x+3. Give the point (x, y).
Need a hint?
- Write an equation for each fact.
- Solve the system for both unknowns.
C4
Solve the system: y=-x+8 and y=2x-4. Give the point (x, y).
Need a hint?
- Write an equation for each fact.
- Solve the system for both unknowns.
Apply
Apply (4)
A1
Solve the system: y=2x-1 and y=3x+0. Give the point (x, y).
Need a hint?
- Write an equation for each fact.
- Solve the system for both unknowns.
A2
Solve the system: y=2x-1 and y=-x+8. Give the point (x, y).
Need a hint?
- Write an equation for each fact.
- Solve the system for both unknowns.
A3
Solve the system: y=-x+1 and y=2x+10. Give the point (x, y).
Need a hint?
- Write an equation for each fact.
- Solve the system for both unknowns.
A4
Solve the system: y=-x+7 and y=-2x+9. Give the point (x, y).
Need a hint?
- Write an equation for each fact.
- Solve the system for both unknowns.
Extension
Extension (4)
E1
Solve the system: y=x+3 and y=-x-1. Give the point (x, y).
Need a hint?
- Write an equation for each fact.
- Solve the system for both unknowns.
E2
Solve the system: y=-2x+6 and y=2x-10. Give the point (x, y).
Need a hint?
- Write an equation for each fact.
- Solve the system for both unknowns.
E3
Solve the system: y=2x-5 and y=-2x+11. Give the point (x, y).
Need a hint?
- Write an equation for each fact.
- Solve the system for both unknowns.
E4
Solve the system: y=2x+1 and y=x+3. Give the point (x, y).
Need a hint?
- Write an equation for each fact.
- Solve the system for both unknowns.