# Video: Solving Simultaneous Equations by Elimination

Use the elimination method to solve the given simultaneous equations 4π₯ β 2π¦ = 4, 5π₯ + 3π¦ = 16.

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### Video Transcript

Use the elimination method to solve the given simultaneous equations. Four π₯ minus two π¦ equals four and five π₯ plus three π¦ equals 16.

Our first step is to either make the coefficients of π¦ or the coefficients of π₯ the same. We could do this by multiplying the top equation by three and the bottom equation by two. This would make the coefficient of the π¦ terms six. Alternatively, we could multiply the top equation by five and the bottom equation by four. This would make the coefficient of π₯ the same. And in this question, they would both be 20π₯.

In this question, we are going to use the first method. Multiplying the top equation by three gives us 12π₯ minus six π¦ equals 12. And multiplying the bottom equation by two gives us 10π₯ plus six π¦ equals 32. We now need to eliminate the π¦ terms. We are going to do this by adding our two equations. Negative six π¦ plus positive six π¦ gives us zero. Adding the π₯ terms gives us 22π₯, and adding the numbers on the right-hand side gives us 44. Dividing both sides of this equation by 22 gives us an π₯-value equal to two, π₯ equals two.

We now need to substitute this value of π₯, π₯ equals two, into one of the equations. 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. In this case, weβre gonna choose five π₯ plus three π¦ equals 16, as all our terms are positive. Substituting in π₯ equals two gives us five multiplied by two plus three π¦ equals 16. As five multiplied by two is 10, this can be rewritten as 10 plus three π¦ equals 16. We then need to balance this equation to work out our value of π¦. Firstly, subtracting 10 from both sides of the equation leaves us with three π¦ equals six as 16 minus 10 equals six. Finally, dividing both sides of this equation by three gives us a π¦-value also equal to two.

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.

This could also be demonstrated on a coordinate axes by plotting the two linear equations. 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.