WEBVTT
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Use the elimination method to solve the given simultaneous equations.
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Four π₯ minus two π¦ equals four and five π₯ plus three π¦ equals 16.
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Our first step is to either make the coefficients of π¦ or the coefficients of π₯ the same.
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We could do this by multiplying the top equation by three and the bottom equation by two.
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This would make the coefficient of the π¦ terms six.
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Alternatively, we could multiply the top equation by five and the bottom equation by four.
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This would make the coefficient of π₯ the same.
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And in this question, they would both be 20π₯.
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In this question, we are going to use the first method.
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Multiplying the top equation by three gives us 12π₯ minus six π¦ equals 12.
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And multiplying the bottom equation by two gives us 10π₯ plus six π¦ equals 32.
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We now need to eliminate the π¦ terms.
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We are going to do this by adding our two equations.
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Negative six π¦ plus positive six π¦ gives us zero.
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Adding the π₯ terms gives us 22π₯, and adding the numbers on the right-hand side gives us 44.
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Dividing both sides of this equation by 22 gives us an π₯-value equal to two, π₯ equals two.
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We now need to substitute this value of π₯, π₯ equals two, into one of the equations.
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We can choose any of the four equations here: four π₯ minus two π¦ equals four, five π₯ plus three π¦ equals 16, or the two below that.
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In this case, weβre gonna choose five π₯ plus three π¦ equals 16, as all our terms are positive.
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Substituting in π₯ equals two gives us five multiplied by two plus three π¦ equals 16.
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As five multiplied by two is 10, this can be rewritten as 10 plus three π¦ equals 16.
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We then need to balance this equation to work out our value of π¦.
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Firstly, subtracting 10 from both sides of the equation leaves us with three π¦ equals six as 16 minus 10 equals six.
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Finally, dividing both sides of this equation by three gives us a π¦-value also equal to two.
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Therefore, the solution to the pair of simultaneous equations four π₯ minus two π¦ equals four and five π₯ plus three π¦ equals 16 are: π₯ equals two and π¦ equals two.
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This could also be demonstrated on a coordinate axes by plotting the two linear equations.
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The point of intersection would be the ordered pair or coordinate two, two as the π₯-coordinate would be two and the π¦-coordinate would also be two.