Quadratic Simultaneous Equations

Question 1

List a step by step process of how to solve quadratic simultaneous equations.

Answer 1

1) rearrange to equal x or y
2) substitute the value into an equation
3) expand the brackets, remember (x - y)² is actually (x-y)(x-y).
4) move all the terms to one side
5) simplify if possible
6) factorise
7) substitute to find the other value

Question 2

Solve: x² + y² = 5

x + y = 3

Answer 2

x + y = 3
x = 3 - y

(3 - y)² + y² = 5
(3 - y)(3 - y) + y² = 5
9 + y² - 3y - 3y + y² = 5
2y² - 6y + 9 = 5
2y² - 6y + 4 = 0

y² - 3y + 2 = 0
(y - 2)(y - 1) = 0

y = 2 or 1

x + y = 3
x + 2 = 3
x = 1, y = 2

x + 1 = 3
x = 2, y = 1

x²+ y² = 5
1 + 4 = 5
4 + 1 = 5

Question 3

Solve: y = x + 3

y = x² + 3x

Answer 3

x + 3 = x² + 3x
x² + 2x - 3 = 0

(x - 1)(x + 3) = 0
x = 1 or -3

y = x + 3
y = 4, x = 1
y = 0, x = -3

y = x² + 3x
4 = 1 + 3
0 = 9 - 9