How would I solve y=3x, 2x+y=5 using the substitiution method?

y=3x (1)

2x+y = 5 (2)

Here we are being asked to find what the value of x and y is. It is asking us to substitute either x or y into the equation to help us find our solution. Now substitue means remove something and replace it with something else. In this case its is asking us to either remove x or y term and replace it with the other term.

So for this question we will take out the y term in equation (2) and put the equivalent x term back in its place. We have chosen to replace the y term in this case because it is the most simple substitution. A good rule in maths is its often best to choose the method that has the least number of steps in as that way there is less chance for accidental errors occuring.

Equation (1) tells us that y=3x, that is 1 y term is equal to 3 x  terms.

Substituting this into equation (2) gives us:


Its possible to add these 'x' terms together to simplify our equation even further, giving us:


Now our aim is to find what 1 x term is. So we need to find a way of getting the x term all alone on one side of the equation, and all other terms on the other side.

It is possible to divide through our equation by 5, giving:


simplifying to:


Now that we've found the value of x we can replace all the x's in our equations to find the value of y. Choosing the simpler equation (1) again we have:


(replacing x with 1 gives:)


simplifying to:


We now have our complete solution. Before we finish though, re-writing our solutions next to each other is thought to be the clearest way of presenting our answer. So we would put:

x=1 , y=3

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