The right tool
Solved for y → substitute. Lined-up standard form → eliminate. Want a picture → graph.
Why it works
Pick what’s least work.
Linear · Systems of equations · 4.6
Choosing a method.
All three methods give the same answer — pick the cleanest. Graphing shows the picture; substitution suits a solved-for-y equation; elimination suits lined-up standard forms.
See it work.
Watch the method
Choosing a method
Same answer — choose the easiest method.
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
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Answer:
The idea underneath.
From easy to tricky.
Solve the system: y=2x-1 and y=-x-4. Give the point (x, y).
1
The system
Two lines — the solution is the point on both. y = 2x - 1;\; y = -x - 4
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+0 and y=2x+8. Give the point (x, y).
1
The system
Two lines — the solution is the point on both. y = -2x;\; y = 2x + 8
2
Substitute one equation into the other
Solve for x, then back-substitute for y. x = -2
3
The solution
Write the intersection point. (-2, 4)
Solve the system: y=-2x+3 and y=-x+4. Give the point (x, y).
1
The system
Two lines — the solution is the point on both. y = -2x + 3;\; y = -x + 4
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, 5)
Where students slip.
Trap
Forcing graphing for ugly numbers.
Fix
Use algebra when the intersection isn’t on grid lines.
Trap
Mixing methods mid-solve.
Fix
Pick one and finish it.
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=2x-8 and y=-x+1. Give the point (x, y).
Need a hint?
- Look at how the system is written.
- Pick the cleanest method.
C2
Solve the system: y=-2x+2 and y=2x-6. Give the point (x, y).
Need a hint?
- Look at how the system is written.
- Pick the cleanest method.
C3
Solve the system: y=2x-3 and y=x+1. Give the point (x, y).
Need a hint?
- Look at how the system is written.
- Pick the cleanest method.
C4
Solve the system: y=x+5 and y=2x+6. Give the point (x, y).
Need a hint?
- Look at how the system is written.
- Pick the cleanest method.
Apply
Apply (4)
A1
Solve the system: y=x+6 and y=2x+8. Give the point (x, y).
Need a hint?
- Look at how the system is written.
- Pick the cleanest method.
A2
Solve the system: y=-2x+7 and y=x+1. Give the point (x, y).
Need a hint?
- Look at how the system is written.
- Pick the cleanest method.
A3
Solve the system: y=-2x-6 and y=2x+2. Give the point (x, y).
Need a hint?
- Look at how the system is written.
- Pick the cleanest method.
A4
Solve the system: y=-x+8 and y=2x-1. Give the point (x, y).
Need a hint?
- Look at how the system is written.
- Pick the cleanest method.
Extension
Extension (4)
E1
Solve the system: y=-2x+7 and y=2x+3. Give the point (x, y).
Need a hint?
- Look at how the system is written.
- Pick the cleanest method.
E2
Solve the system: y=x-5 and y=-3x+7. Give the point (x, y).
Need a hint?
- Look at how the system is written.
- Pick the cleanest method.
E3
Solve the system: y=2x-1 and y=x+0. Give the point (x, y).
Need a hint?
- Look at how the system is written.
- Pick the cleanest method.
E4
Solve the system: y=2x-5 and y=-2x+11. Give the point (x, y).
Need a hint?
- Look at how the system is written.
- Pick the cleanest method.