Answer the following simultaneous equation:

Equation 1) x² +y²=5  (Equation 2) y=3x+1

The value of x is the same in both equations, as is the value of y. Therefore we can use one to work out the other. for example taking equation 1 and definining x in terms of y by rearranging the equation.

x² +y²=5

y=3x+1

Equation 2 tells us what y is, so we can put that into equation 1 Therefore...

x² + (3x+1)(3x+1) = 5

...then expand the brackets

x² + 9x² +3x +3x +1 = 5

...then group the factors

10x² +6x +1 =5, then get the equation to equal 0 so we can factorise... 10x² +6x -4 = 0

(5x-2)(2x+2)

5x-2=0 or 2x+2=0

5x=-2 or 2x=-2

x=-2/5 or x=-1

we know that x=-1 as x and y are whole numbers in this equation. Therefore, to check this we put x back into the original equations to find out the value of y.

y=3x+1.... y=3(-1)+1..... y=-2

So put the values of x and y into equations 1 to check these values...

x² +y²=5

(-1)²+ (-2)²=5

as 1 +4 =5

Now we know the values of x and y are corect