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### Solve the simultaneous equations: 5x + 3y = 9 and 7x - 2y = 25.

To solve these similar equations, we must either first eliminate x or y. There are multiple ways of doing this, one being rearranging one of the equations so that it is either "x=.." or "y=..." and then substituting the rearranged equation into the other equation and so eliminating one variable.

Specifically for this example it could be:

Rearrange 7x - 2y = 25 to 2y = 7x - 25. Then divide the entire equation by 2, giving: y = (7/2)x - (25/2).

Now enter this new equation into the second equation in place of y and solve for x: 5x + 3y = 9 becomes 5x+3(3.5x - 12.5) = 9. Rearrange by first expanding the brackets and collecting all x on one side and then dividing by the coefficient of x to give x = 3.

Now enter this into an equation and solve for y. For instance: 5x + 3y = 9, set x=3 giving 5(3) + 3y = 9. 3y=(-6) Y=(-2)

you can check this but entering both these values for x and y into the second equation for example. 7(3)-2(-2)= 25

21- (-4) = 25. Therefore this is the correct solution.

11 months ago

Answered by Màiri, who has applied to tutor GCSE Maths with MyTutor

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