How do you solve the following simultaneous equations? 4x-3y=18, 7x+5y=52

First, we need to try and eliminate one of the x or the y variables from both equations. Here, we are going to eliminate the y variable. In order to do this, we need to make the y coefficients equal in both equations, and we can do this by multiplying the first equation through by 5 and the second one through by 3, so that both y variables are equal to 15. We get:

20x-15y=90 21x+15y=156

If we add the two equations together, we will eliminate the y variable, as required, because -15+15=0. Hence, we are left with one equation in terms of x:

41x=246, so x=6.

We can substitute this result into the first equation to get: 120-15y=90, and we can solve this to get y=2.

Hence, the solution to the simultaneous equations is x=6 and y=2.

Answered by Alma O. Maths tutor

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1 a. If x=6a+3 and a is 4 what is x? b. Make a the subject of the formula.


Solve the simultaneous equations 1) 3x + 2y = 4 & 2) 4x + 5y = 17


Solve 3x – 5 < 16


Factorise and thus solve: x^2– 2x– 24 = 0


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