# Solve this pair of simultaneous equations (1) 5x+2y=20 and (2) x+4y=13

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To solve these equations, our aim is to find a value of x and a value of y that satisfy both equations at the same time. By satisfy we mean, if we plug our values in for x and y then the left hand side and right hand side of each equation will equal eachother.

First to find x and y we must try and eliminate either x or y to find the other.

Lets try and eliminate x.

We can write equation (2) with x as the subject by subtracting 4y from both sides, like so:

x=13-4y

Now we can substitute this into equation (1) to eliminate x giving:

5(13-4y) + 2y = 20

Expanding the brackets gives

65 - 20y + 2y = 20

Now we collect all the y's onto one side and the constants onto the other giving:

45 = 18y

Then divide through by 18 to give y=5/2

Now we substitute this into either equation (1) or (2) for y to find x.

With (1) : 5x + 2(5/2) = 20, 5x = 15, x=3

With (2) : x + 4(5/2) = 13, 5x=15, x=3

So our solution is x=3, y=5/2. It isn't necessary to show x's value with both equations but it can be useful to check your answer is correct!

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