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
