# Solve the simultaneous equations y= 3x +4 and y= 2x + 5

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'Solve' means to find the values of the unknown variables in the equations, commonly letters, which in this question are x and y.

Step 1: Put equations equal to eachother

Both equations given are equal to y (written in the form y=), therefore we can put the parts containing x of the equations equal to each other, giving 3x+4 = 2x+5

Step 2: Collect 'like' terms

All this means is to get all of the terms containing x (or letter given in the question) on one side, and all the numbers on the other side.

So in this example, to get all the x's on one side we can subtract 2x from both sides giving x+4 = 5.

And to get all the numbers on the other side, we can subtract 4 to both sides giving x=1

Step 3: Solve

In this example, we have already managed to find out the value of x from step 2 (x=1)

To find out y, we can substitute in our calculated x value into any of the equations given (it is usually quicker and easier to use the equation with smaller numbers!)

So, using the second equation, and substituting in x=1, we can calculate the value of y.

y = 2(1)+ 5 = 2+ 5 = 7  giving y=7

Step 4: Check

In an exam, if you have time, it is always worth checking you have calculated the correct answers!

This is easy, just substitute your calculated values of x and y into both equations, and if correct, then each side will be equal to each other.

For example:

7 = 3(1) +4  = 3 + 4 = 7

7 = 2(1) + 5 = 2 + 5 = 7

Both sides are equal to each other therefore this is correct!

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