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Lesson · Grade 10 · Foundations of Mathematics and Pre Calculus

Solving a System by Substitution

  • Grade 10
  • Foundations of Mathematics and Pre Calculus
  • 2 min 14 s
  • British Columbia
  • BC10-MA-25

Using the system y = 2x − 1 and 3x + y = 14, the video explains what a system of linear equations, a solution and solving by inspection are, then puts 2x − 1 in place of y and solves 3x + 2x − 1 = 14 step by step to get x = 3. It warns that stopping at x is a common mistake, finds y = 5, checks the pair in both equations, and ends on the ordered pair (3, 5) with a one-line recap: substitute, solve for x, find y, check both.

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In one sentence

The question this lesson answers

Let us solve this system: y equals 2x minus 1, and 3x plus y equals 14.

A system of linear equations is a set of straight line equations that share unknowns, here x and y.

Transcript

What the lesson says

Let us solve this system: y equals 2x minus 1, and 3x plus y equals 14.

A system of linear equations is a set of straight line equations that share unknowns, here x and y.

A solution is a pair of values for x and y that makes both equations true at once.

If the answer is easy to spot, solve by inspection: look for the answer, then test your guess.

Substitution means replacing a letter with an expression equal to it. Equation 1 says y equals 2x minus 1.

In equation 2, put 2x minus 1 in place of y: 3x plus y equals 14 becomes 3x plus 2x minus 1 equals 14.

3x and 2x are like terms: both are a number times x. Together they make 5x, so 5x minus 1 equals 14.

Add 1 to both sides, so 5x equals 15.

Divide both sides by 5, so x equals 3.

A common mistake is to stop here, but the solution also needs y.

Put 3 in place of x in equation 1: y equals 2 times 3 minus 1, which is 6 minus 1, so y equals 5.

Now check both equations. In equation 1, 2 times 3 minus 1 is 6 minus 1, which is 5. That matches y.

In equation 2, 3 times 3 plus 5 is 9 plus 5, which is 14. That matches too.

Both are true, so the solution is x equals 3 and y equals 5: the ordered pair 3, 5, with x written first.

To recap: substitute, solve for x, find y, and check both equations.

Curriculum

Where this fits

British Columbia, Grade 10

Foundations of Mathematics and Pre Calculus 10, Linear relations: systems of linear equationsBC10-MA-25

Previous: Solving a System by Graphing: The Point Both Lines ShareNext: Solving a System by Elimination

The outcomes and strands follow the British Columbia curriculum.

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