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Solve these simultaneous equations. 5x + 2y = 20 and x + 4y = 13.

(1) 5x + 2y = 20

(2) x + 4y = 13

Step 1: Eliminate x or y. We do this but making either the x or y terms the same, in this example, I will make the y terms the same, by multiplying the first equation by 2.

(1) X 2 = 10x + 4y = 40. Let's call this equation (3).

We can now take equation (2) away from (3).

   10x + 4y = 40
_    x + 4y = 13

9x = 27

Step 2: Divide both sides by 9 to get x on its own.
x = 3.

Step 3: Substitute x into equation (1) or (2). 
For example, if you substitute it into equation (2) you get: 3 + 4y = 13.

Step 4: Rearrange to find y. 4y = 10
y = 2.5

Step 5: Check your answer by substiting your values for x and y into equation (1) or (2).

Equation 1: 5(3) + 2(2.5) = 20
15 + 5 = 20

The left hand side equals the right hand side, so you have found x and y!

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