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GB-20-04-001 · Linear and quadratic equations

Solve the simultaneous equations
y=x2y=x^2
y=2xy=2x

Simultaneous Equations: Quadratic & Linear Booklet p. 28
Method
1) Substitute the linear equation into the quadratic
2) Rearrange to zero
3) Factorise with a grid
4) Solve and substitute back to pair the coordinates
Worked Example (GB-20-04-001)
1)
Substitute the linear expression for y into the quadratic: x2=2x+0x^2=2x + 0.
2)
Rearrange to zero: x2−2x=0x^2 - 2x=0.
3)
Take out the common xx using the lowest power (p. 4).
4)
×xx−2-2
xxx2x^2−2x-2x
5)
x−2=0⇒x=2x - 2=0\quad\Rightarrow\quad x=2
6)
x+0=0⇒x=0x + 0=0\quad\Rightarrow\quad x=0
7)
Substitute x=2x=2 into the line: y=(2)(2)+0=4y=(2)(2) + 0=4; point (2,4)(2,4).
8)
Substitute x=0x=0 into the line: y=(2)(0)+0=0y=(2)(0) + 0=0; point (0,0)(0,0).
Ans = (x,y)=(0,0)(x,y)=(0,0) or (2,4)(2,4)