Solve these simultaneous equations: y=3x-10; y=2x+5

Method 1 (algebraically):

Since we have "y=" at the start of both equations, we can substitue one into the other to get

3x-10=2x+5

Then we want all the x terms on one side of the equation, and all the number terms on the other side. So we can subtract 2x from both sides to get

x-10=5

then add 10 to both sides to get

x=15.

Now we can substitute this x value back into our first equation to find a value for y!

So y=3(15)-10=45-10=35

Then we check that our x and y values (x=15 and y=35) satisfy our second equation.

35=2(15)+5

They do, so we have our answer!

Method 2 (graphically):

​If you have graph paper, and can draw accurately enough, you can draw the two equations as graphs (on the same piece of paper) and find the co-ordinates of the point where they cross.

Ideally, we want you to able to solve equations like this using algebra, however being able to draw the graph allows you to visualise what is happening.