Question

Solve the simultaneous equation: y=2x²+3x-31 y= x= 21-2x​

Answer 1

1. x =(3-√257)/4=-3.258

2. x =(3+√257)/4= 4.758

Explanation:

irst add

x

to both sides of the second equation to get:

y = x + 3

Then substitute this expression for y into the first equation to get:

29 = x 2 + ( x + 3 ) 2 = 2 x 2 + 6 x + 9

Subtract 29 from both ends to get:

0 = 2 x 2 + 6 x − 20

Divide both sides by 2 to get:

0 = x 2 + 3 x− 10 = ( x+ 5 ) ( x − 2 )

So x = 2 or x = − 5

If x = 2 then y = x + 3 = 5 .

If x = − 5 then y=x + 3 = − 2

So the two solutions

( x, y ) are ( 2 , 5 ) and ( − 5 , − 2 )