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

'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!