courses › Algebra

Two equations, two unknowns, one answer.

Pen and paper is fine · no calculator needed why?

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Opens at level 24.

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Builds on: Lines & slope (not open yet)

skills · practice stats

From rounds of this course only: box, review and trial answers are left out. Once a skill has 40 tries, it compares your first 20 tries with your last 20.

• Solve by elimination par 30 s not tried yet

  worked example

  Solve the system: −x − 3y = −6 −x − 4y = −8 Enter x, y.

  Answer: (0, 2)

  1. Subtract the second equation from the first: y = 2.
  2. Put y = 2 into the first equation: −x = −6 − (−6) = 0, so x = 0.

• Solve by substitution par 40 s not tried yet

  worked example

  Solve the system: y = 2x + 4 3x + 5y = −19 Enter x, y.

  Answer: (-3, -2)

  1. Substitute: 3x + 5(2x + 4) = −19.
  2. So 13x + 20 = −19, which gives 13x = −39.
  3. x = −3, and y = 2 × (−3) + 4 = −2.

• Two-item word problem par 45 s not tried yet

  worked example

  A café sells large coffees for $5 and small coffees for $4. One morning it sold 58 coffees for $276. How many large coffees did it sell?

  Answer: 44

  1. Let l be the number of large coffees, so 58 − l are small coffees: 5l + 4(58 − l) = 276.
  2. That gives l + 232 = 276, so l = 276 − 232 = 44.

rest ladder

Win 3 of your last 4 rounds and the course rests. A win is 90% right, within 2× the round's par. Pass the review when it comes back and the next rest is longer.

1. 1 day
2. 3 days
3. 7 days
4. 14 days
5. 30 days
6. 60 days
7. mastered · every 90 days

your rounds

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