Solve the simultaneous equation

Question

 

y=10-x and y=2x^2+4?

Answer 1

y = 10 - x and y = 2x² + 4

i.e. 10 - x = 2x² + 4

Subtract 10 from each side.

- x = 2x² - 6

Add 'x' to each side.

2x² - 6 + x = 0.

2x² + x - 6 = 0.

Now solve the equation using factor method.

2x² + 4x - 3x - 6 = 0

2x(x + 2) - 3(x + 2) = 0

(2x - 3)(x + 2) = 0

2x - 3 = 0 or x + 2 = 0

Take 2x - 3 = 0

Add 3 to each side.

2x = 3.

Divide each side by 2.

x = 3/2

Take x + 2 = 0.

Subtract 2 from each side.

x = -2.

Therefore x = -2 or 3/2.

Substitute x = -2 and x = 3/2 in the 1st equation.

If x = -2 then y = 10 - (-2) = 10+2 = 12.

If x = 3/2 then y = 10 - (3/2) = (20-3) / 2 = 17/2.

The solutions are (-2, 12)(3/2, 17/2).