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EQAO Grade 9 Math — free MCQ practice

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EQAO Grade 9 Math subjects

Mathematics (21)

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Systems of Linear Equations in Two VariablesApplying Linear Systems to Situations

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What counts as the solution to a system of two linear rules in two unknowns?Read the answer and worked solution →Check the pair x = 4, y = 3 against this system: 2x + 5y = 23 and 3x - y = 9.Read the answer and worked solution →The two rules in a system turn out to describe the very same line. How many pairs of values solve the system?Read the answer and worked solution →What is the first step of the substitution method for a system of two rules in two unknowns?Read the answer and worked solution →

Worked practice questions

What counts as the solution to a system of two linear rules in two unknowns?

  1. Any value of x that makes the first rule true
  2. Any pair of values that fits either rule alone
  3. The point where each line meets the sideways axis
  4. A pair of values that fits both rules at once
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Correct answer: D. A pair of values that fits both rules at once

1. A system in two unknowns needs a value for each unknown, so a solution is a pair rather than a single number. 2. That pair has to satisfy each rule on its own, not just one of them. 3. Option B drops the word both, which is the whole point of a system. 4. So the solution is a pair of values that fits both rules at once, option D. _Source: OpenStax College Algebra (CC BY 4.0), Ch 7 "Systems of Equations and Inequalities", section 7.1 Systems of Linear Equations: Two Variables_

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Check the pair x = 4, y = 3 against this system: 2x + 5y = 23 and 3x - y = 9.

  1. It is the solution, since both come out true
  2. It fails, since only the first comes out true
  3. It fails, since only the second comes out true
  4. It fails, since neither one comes out true
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Correct answer: A. It is the solution, since both come out true

1. Put x = 4 and y = 3 into the first rule: 2 times 4 is 8, and 5 times 3 is 15. 2. Adding gives 8 plus 15, which is 23, and the first rule asked for 23, so it holds. 3. Put the same pair into the second rule: 3 times 4 is 12, and 12 minus 3 is 9. 4. The second rule asked for 9, so it holds as well. 5. A pair that satisfies both rules is the solution, option A. _Source: OpenStax College Algebra (CC BY 4.0), Ch 7 "Systems of Equations and Inequalities", section 7.1 Systems of Linear Equations: Two Variables_

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The two rules in a system turn out to describe the very same line. How many pairs of values solve the system?

  1. Infinitely many, since every point on it fits
  2. Exactly one, where the line meets itself
  3. None, because a line cannot cross itself
  4. Exactly two, one at each end of the line
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Correct answer: A. Infinitely many, since every point on it fits

1. A solution is a point lying on both lines. 2. If the two rules describe one line, then every point on that line lies on both of them. 3. A line holds endlessly many points, so there are endlessly many solutions. 4. Such a system is called dependent. 5. Option B treats the overlap as a single crossing, but the lines overlap everywhere rather than at one place. _Source: OpenStax College Algebra (CC BY 4.0), Ch 7 "Systems of Equations and Inequalities", section 7.1 Systems of Linear Equations: Two Variables_

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