Lesson · Grade 10 · Foundations of Mathematics and Pre Calculus
Solving a System by Elimination
- Grade 10
- Foundations of Mathematics and Pre Calculus
- 2 min 34 s
- British Columbia
- BC10-MA-26
The video solves 2x + 3y = 12 and 4x − 3y = 6 by adding the equations so the y terms cancel, which gives 6x = 18 and x = 3. It then substitutes to get y = 2 and checks the answer in the second equation. It goes on to x + 2y = 7 and 3x + y = 11, multiplies every term of the first equation by 3 (showing the common mistake of leaving the 7 alone), subtracts to get 5y = 10, finds x = 3, checks it, and ends on a one-line recap: opposite coefficients add, equal coefficients subtract.
Anyone can watch two lessons on the website without an account. Signing in is free, no payment and no card, and opens three a day; Plus has no limit.
Loading
In one sentence
The question this lesson answers
A system of linear equations is a set of equations in the same unknowns, here x and y.
To solve it, find the values of x and y that make both equations true.
Transcript
What the lesson says
A system of linear equations is a set of equations in the same unknowns, here x and y.
To solve it, find the values of x and y that make both equations true.
Elimination adds or subtracts the equations to remove one unknown.
The y coefficients, the numbers in front of y, are 3 and negative 3.
They are opposites, so add: 2x plus 4x is 6x, 3y plus negative 3y is 0, 12 plus 6 is 18.
The y terms cancel: 6x equals 18. Divide both sides by 6, so x equals 3.
Now substitute: put 3 in place of x in the first equation.
2 times 3 is 6. Subtract 6, so 3y equals 6. Divide by 3, so y equals 2.
Check in the second equation: 4 times 3 minus 3 times 2 is 12 minus 6, which is 6. So x is 3 and y is 2.
Next: x plus 2y equals 7, and 3x plus y equals 11. Nothing cancels yet.
Multiply the whole first equation by 3 to match the 3x: x becomes 3x, 2y becomes 6y, 7 becomes 21.
A common mistake is multiplying only part, like not multiplying the 7. That makes a different equation.
Both have 3x now, so subtract: 3x minus 3x is 0, 6y minus y is 5y, 21 minus 11 is 10.
That leaves 5y equals 10. Divide both sides by 5, so y equals 2.
Substitute y equals 2 into x plus 2y equals 7: x plus 4 equals 7, so x equals 3.
Check in the second equation: 3 times 3 plus 2 is 9 plus 2, which is 11. So again x is 3 and y is 2.
Recap: make the coefficients of one unknown opposite or equal, then add or subtract to eliminate it.
Curriculum
Where this fits
- British Columbia, Grade 10
Foundations of Mathematics and Pre Calculus 10, Linear relations: systems of linear equationsBC10-MA-26
Previous: Solving a System by SubstitutionNext: Writing and Solving a System from a Word Problem
The outcomes and strands follow the British Columbia curriculum.
Keep going
2 min 18 sAdding an Arithmetic Series by Pairing Terms
Grade 10 · 2 min 18 s
2 min 11 sArithmetic Sequences Are Linear: The Common Difference Is the Slope
Grade 10 · 2 min 11 s
2 min 4 sArithmetic sequences: first term and common difference
Grade 10 · 2 min 4 s
2 min 8 sFour Kinds of Slope: Uphill, Downhill, Flat and a Wall
Grade 10 · 2 min 8 s
2 min 16 sGeneral form, and changing between the forms of a line
Grade 10 · 2 min 16 s
2 min 1 sHorizontal and vertical lines: y = 3 and x = −2
Grade 9 · 2 min 1 s
2 min 5 sParallel and perpendicular lines: equal slopes and negative reciprocals
Grade 10 · 2 min 5 s
2 min 4 sPoint-slope form: a line from one point and its slope
Grade 10 · 2 min 4 s
- All Grade 10 Foundations of Mathematics and Pre Calculus lessons
- Create a free account to watch three lessons a day, no payment and no card.