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Simultaneous Quadratic Equations

Hi, need help with this, I have no idea how to work it out

y = 3 x + 2
y = x² + 6 x + 4

x = and y = or x = and y =

Any advice on how to go about solving this?

Reply 1

Revolution is my Name

You have two expressions in terms of x that both equal y. What can you then say about the relationship between those two expressions?

Reply 2

nk9230

philg89

Hi, need help with this, I have no idea how to work it out

y = 3 x + 2
y = x² + 6 x + 4

x = and y = or x = and y =

Any advice on how to go about solving this?

Set them equal to each other, move all the terms to one side.... get where I am going with this?

Reply 3

steve2005

philg89

Hi, need help with this, I have no idea how to work it out

y = 3 x + 2
y = x² + 6 x + 4

x = and y = or x = and y =

Any advice on how to go about solving this?

Substitute 3x + 2 for y in equation 2.

Rearrange so that it equals zero, factorise or complete the square.

Reply 4

The Referee

Put the equations equal to each other:

3x + 2 = x^2 + 6x + 4

Move everything to the same side:

x^2 + 3x + 2 =0

factorise and solve or use the quadratic equation for each x value then insert and solve for y