The full routine
Define variables, write two equations, solve, and interpret the solution.
Why it works
Story → two equations → point.
Linear · Apply · 5.3
Apply mastery.
Mixed practice: translate the situation into two equations, choose a method, solve, and check both answers make sense in context.
See it work.
Watch the method
Apply mastery
Translate, solve, and interpret both answers.
1
The system
Two lines — the solution is the point on both.
2
Substitute one equation into the other
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).
streak 0
best 0
…
Answer:
The idea underneath.
From easy to tricky.
Solve the system: y=-x-4 and y=-2x-5. Give the point (x, y).
1
The system
Two lines — the solution is the point on both. y = -x - 4;\; y = -2x - 5
2
Substitute one equation into the other
Solve for x, then back-substitute for y. x = -1
3
The solution
Write the intersection point. (-1, -3)
Solve the system: y=-2x+11 and y=-x+7. Give the point (x, y).
1
The system
Two lines — the solution is the point on both. y = -2x + 11;\; y = -x + 7
2
Substitute one equation into the other
Solve for x, then back-substitute for y. x = 4
3
The solution
Write the intersection point. (4, 3)
Solve the system: y=2x-5 and y=3x-9. Give the point (x, y).
1
The system
Two lines — the solution is the point on both. y = 2x - 5;\; y = 3x - 9
2
Substitute one equation into the other
Solve for x, then back-substitute for y. x = 4
3
The solution
Write the intersection point. (4, 3)
Where students slip.
Trap
Rushing the setup.
Fix
A careful pair of equations makes solving easy.
Trap
Not checking the answer.
Fix
Substitute back into both.
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-4 and y=-2x-5. Give the point (x, y).
Need a hint?
- Set up two equations.
- Solve and check both.
C2
Solve the system: y=x-4 and y=-2x-1. Give the point (x, y).
Need a hint?
- Set up two equations.
- Solve and check both.
C3
Solve the system: y=-x+5 and y=-2x+6. Give the point (x, y).
Need a hint?
- Set up two equations.
- Solve and check both.
C4
Solve the system: y=-x+2 and y=3x-10. Give the point (x, y).
Need a hint?
- Set up two equations.
- Solve and check both.
Apply
Apply (4)
A1
Solve the system: y=2x-3 and y=-2x+1. Give the point (x, y).
Need a hint?
- Set up two equations.
- Solve and check both.
A2
Solve the system: y=-2x-7 and y=-3x-10. Give the point (x, y).
Need a hint?
- Set up two equations.
- Solve and check both.
A3
Solve the system: y=x-3 and y=-x+5. Give the point (x, y).
Need a hint?
- Set up two equations.
- Solve and check both.
A4
Solve the system: y=x+2 and y=-x-4. Give the point (x, y).
Need a hint?
- Set up two equations.
- Solve and check both.
Extension
Extension (4)
E1
Solve the system: y=2x-5 and y=-2x-1. Give the point (x, y).
Need a hint?
- Set up two equations.
- Solve and check both.
E2
Solve the system: y=-x+6 and y=x-2. Give the point (x, y).
Need a hint?
- Set up two equations.
- Solve and check both.
E3
Solve the system: y=-x+4 and y=2x+7. Give the point (x, y).
Need a hint?
- Set up two equations.
- Solve and check both.
E4
Solve the system: y=2x+4 and y=3x+7. Give the point (x, y).
Need a hint?
- Set up two equations.
- Solve and check both.