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EQAO Grade 9 Math Systems of Linear Equations in Two Variables — practice questions

Explore 15 free Systems of Linear Equations in Two Variables questions in EQAO Grade 9 Math Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Systems of Linear Equations in Two Variables questions and exercises with answers

Showing questions 1–15 of 15.

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 →Substitution is easiest when one of the two rules has a particular feature. What is that feature?Read the answer and worked solution →Solve this system by substitution: y = x - 4 and 3x + 2y = 22.Read the answer and worked solution →In the system x + 3y = 11 and 2x - y = 8, by what number should the first rule be multiplied so that adding the two rules removes x?Read the answer and worked solution →A pair of values has been worked out for a system. What is the safest way to be sure it is right?Read the answer and worked solution →Can a system of two linear rules in two unknowns have exactly two solutions?Read the answer and worked solution →One rule of a system reads 2x + 6y = 10 and the other reads x + 3y = 5. What kind of system is this?Read the answer and worked solution →Solve this system by adding the rules: 4x + y = 19 and 4x - 3y = 7.Read the answer and worked solution →Drag each pair to how the lines sitRead the answer and worked solution →Knock out the false claims on 0 = 0Read the answer and worked solution →Order the substitution stepsRead the answer and worked solution →Split no solution from many solutionsRead 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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More Mathematics topics

Applying Linear Systems to Situations