1. Simultaneous Equations 1
2x + y = 3 and 3x + y = 5
2x + y = 3
3x + y = 5
The y coefficient of both equations is 1 so eliminate y
subtract
2x – 3x = 3 - 5
-x = -2
In both equations the sign of y is the same so subtract
x = 2
2x + y = 3
2(2) + y = 3 so 4 + y = 3 so
y = 3 - 4
So y = -1
Ans x = 2, y = -1

2. Quadratic + linear 2 1. Rearrange first equation to read x = or y =
2x + 3y = 1 and xy = -2
2. Replace this variable in the second equation
x = 1 – 3y xy = -2 2
(1 – 3y ) y = -2 2
3. Multiply out and solve
y – 3y2 = -4 so 3y2 – y –4 = 0 so y = -1 and 4/3
4. Find the two pairings
When y = -1, x = 2 and when y = 4/3 x = -3/2
Solutions ( 2, -1 ) and ( -3/2, 4/3)

3. Quadratic + linear 3 1. Rearrange second equation to read x = or y =
x2 + y2 = 5 and y-x = 1
2. Replace this variable in the second equation
y = 1 + x and x2 + y2 = 5
x2 +
(1 + x)2 = 5
x x + x2 = 5
3. Multiply out, put equal to 0, and solve
2x2 + 2x – 4 = 0
x = -2  (22 – (4*2*-4)) =
2* 2
-2  (4+32) = 4
-2  6 = 4
1 or -2
When x = 1, y = 2 and when x= -2, y = -1
4. Find the two pairings
Solutions (- 2, -1 ) and ( 1, 2)