How would I solve this set of simultaneous equations using the elimination method?

Solve the following equations for x and y:

x + 2y = 4

2x + 3y = 7

We are going to solve this using the elimination method. This means that we are going to either add or subtract the equations from each other.

Lets begin by labelling the equations:

x + 2y = 4 <--- Equation 1

2x + 3y = 7 <--- Equation 2

The next step is to make sure we have either the same number of x's or the same number of y's in each equation. Turns out we do not in this example.

So we have multiply one of the equations so that we do have the same number of x's or y's in each equation.

If multiply Equation 1 by 2, we will have the term 2x in the equation. This is will be the same number of x's as in Equation 2. Hurrah!

So multiplying Equation 1 by 2, we get:

2x + 4y = 8 <--- Equation 1

Now we can solve by the equations by elimination, because the number of x's are the same:

2x + 4y = 8 

2x + 3y = 7

But do we add or subtract the equations from each other?

Remember this simple saying: If they have the Same Sign, then Subtract! (Its the alliteration that helps me remember it!)

It turns out these equations indeed have the same sign, so we must subtract!

2x + 4y = 8 

2x + 3y = 7

0 + y = 1 

So we end up with y = 1

Now to solve for x, we must substitute y = 1 into either Equation 1 or Equation 2. Lets try it with Equation 2:

2x + 3y = 7

2x + 3 (1) = 7

2x + 3 = 7

2x = 7 - 3

2x = 4

x = 2

So the answer is x = 2, y =1 


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