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Math and calculus tutoring for LaSalle College Montréal

Get help with the step that's holding you back in calculus, linear algebra, probability or statistics. Work through your questions with a tutor, understand why each method works, and practise applying it yourself.

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Calculus

Your tutor can help you repair an algebra step, choose a derivative rule, interpret a rate of change or decide how to approach an integral.

Linear algebra

Set up a system together, explain an elimination step and check your solution in the original equations.

Probability and statistics

Identify what you're counting or comparing, choose an appropriate method and explain what the result means.

Math in your LaSalle program

Social Science includes Calculus I, Calculus II, linear algebra, quantitative analysis and applied statistics in its published course list. Bring the topic you're working on in your own course.

LaSalle's Social Science course list

Studying computing or artificial intelligence? Tutoring can focus on the foundational mathematics in your course, such as algebra, calculus, probability or statistics. Bring the mathematical question and your attempt.

Try it: solve a system and check both equations

A solution must satisfy both equations at the same time. For real numbers x and y, solve:

{x+2y=83x−y=3\begin{cases}x + 2y = 8\\3x - y = 3\end{cases}

  1. Eliminate x.

    Keep the first equation. Replace the second by the second minus three times the first:

    (3x−y)−3(x+2y)=3−24(3x - y) - 3(x + 2y) = 3 - 24

    −7y=−21-7y = -21

    So y=3y = 3.

  2. Substitute back.

    The first equation becomes x+2(3)=8x + 2(3) = 8, so x=2x = 2.

  3. Check both original equations.

    2+2(3)=82 + 2(3) = 8 and 3(2)−3=33(2) - 3 = 3. The solution is (x,y)=(2,3)(x, y) = (2, 3).

Why this works

We kept the first equation, so adding three times it back to the new second equation recovers the original second equation. The operation is reversible and preserves the shared solutions. When subtracting 3(x+2y)3(x + 2y), subtract both 3x3x and 6y6y.

Your turn

Try each question before opening its answer.

1. Repeat the method

Solve x+2y=8x + 2y = 8 and 3x−y=103x - y = 10.

Hint

Keep the first equation and subtract three times it from the second.

Answer and reasoning

The new second equation is −7y=−14-7y = -14, giving y=2y = 2. Then x+4=8x + 4 = 8 gives x=4x = 4. Check: 4+2(2)=84 + 2(2) = 8 and 3(4)−2=103(4) - 2 = 10.

2. Recognize a contradiction

Can x+2y=8x + 2y = 8 and 2x+4y=172x + 4y = 17 both hold?

Hint

Double the first equation, then compare it with the second.

Answer and reasoning

Subtracting twice the first equation from the second gives 0=10 = 1. No real values of x and y can satisfy that statement, so the system has no solution.

3. Recognize a repeated condition

Replace 17 by 16 in question 2. What changes?

Answer and reasoning

Elimination now gives 0=00 = 0, which adds no restriction. The first equation still has to hold. Choose any real number t for y, then x=8−2tx = 8 - 2t. Thus (x,y)=(8−2t,t)(x, y) = (8 - 2t, t) describes infinitely many solutions. The remaining equation and the free choice of y justify this conclusion.

Keep practising

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Bring your attempt, even if it stops after one line. Your tutor can find the first unclear step with you, explain the method and help you check your answer. Then try a similar question yourself to see whether the method has clicked.

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