This document discusses solving simultaneous linear and quadratic equations. It explains that for a linear equation and a non-linear equation, an unknown can be expressed in terms of the other unknown from the linear equation. This forms a quadratic equation that can then be solved using factorisation or the quadratic formula to obtain the values for both unknowns. As an example, it shows choosing x as the easier unknown from the linear equation x+2y=4 to get x=4-2y, then substituting this into the quadratic equation x^2+xy+y^2=7. This results in a quadratic equation that can be factorised to solve for y and back substitute to find x.

2. Example: 2y-3x=5
Linear equation are equations that have one or
more unknowns in the first degree.
Non linear equations have one or more unknowns
in degrees greater than one.
This is just a meaning, learn how Example: x² + 2x + y² – 3y= 0
to solve equations. This is not
so important. Just get to
know what does the terms mean.

3. The unknown should be
From the linear equation, an
substituted into the non- linear
unknown should be expressed
equation. This forms a quadratic
in terms of other unknown.Let it
equation in terms of other
be “y” or “x”
unknown.
Obtain the values of second Solve the quadratic equation to
unknown by substituting the obtain the values of the first
values of the first unknown unknown using factorisation or
into the linear equation. the quadratic formula.

4. Example: 5. Overall, when y=3, x= -2 and
when y=1, x= 2
Solve the simultaneous equation.
You may choose unknown of
x+2y = 4 “y” but you will get complicated which
x²+xy+y² = 7 y= 4-x
2
1. Choose an easier 2. Use the value of “x” to substitute
unknown from the first equation into second equation to get
to get third equation. the value of y such:
From this question, (4-2y)² + (4-2y)y + y² = 7
unknown of x is easier.
x+2y=4 Factorisation
x= 4 - 2y method
4.Substitute the values of y into the 3. Expand it and you will get
third equation that you formed. y² – 4y + 3 = 0
4 – 2(3) and 4 – 2(1) (y – 3) (y – 1)= 0
You will get x= -2 and 2 y = 3 or y = 1