Solving Simultaneous Equations
1.
3.
5.
7.
9.
11.
Section 1 – Solve the simultaneous equations below
2.
𝑥+𝑦 =9
𝑥+𝑦 =7
𝑥−𝑦 =2
𝑥 + 2𝑦 = 11
4.
𝑥 + 2𝑦 = 9
4𝑥 + 𝑦 = 5
3𝑥 + 𝑦 = 2
𝑥 − 3𝑦 = 11
6.
5𝑥 + 3𝑦 = 8
4𝑥 + 3𝑦 = 0
𝑥 + 3𝑦 = −2
𝑥 + 2𝑦 = 5
Section 2 – Solve the simultaneous equations below
8.
2𝑥 + 3𝑦 = 11
2𝑥 + 4𝑦 = 17
3𝑥 + 5𝑦 = 18
6𝑥 − 2𝑦 = 2
10.
4𝑥 + 2𝑦 = 24
2𝑥 + 2𝑦 = 8
3𝑥 − 3𝑦 = 9
3𝑥 − 3𝑦 = 18
12.
2𝑥 + 3𝑦 = 5
3𝑥 + 5𝑦 = 15
7𝑥 + 4𝑦 = −2
5𝑥 + 3𝑦 = 1
ANSWERS
Solving Simultaneous Equations By Elimination
1.
3.
5.
7.
9.
11.
Section 1 – Solve the simultaneous equations below
2.
𝑥 + 𝑦 = 9 𝒙 = 𝟓. 𝟓
𝑥+𝑦 =7 𝒙=𝟑
𝑥 − 𝑦 = 2 𝒚 = 𝟑. 𝟓
𝑥 + 2𝑦 = 11 𝒚 = 𝟒
4.
𝑥 + 2𝑦 = 9 𝒙 = −𝟏
4𝑥 + 𝑦 = 5 𝒙 = 𝟐
3𝑥 + 𝑦 = 2 𝒚 = 𝟓
𝑥 − 3𝑦 = 11 𝒚 = −𝟑
6.
5𝑥 + 3𝑦 = 8 𝒙 = 𝟐. 𝟓
4𝑥 + 3𝑦 = 0 𝒙 = −𝟑
𝑥 + 3𝑦 = −2 𝒚 = −𝟏. 𝟓
𝑥 + 2𝑦 = 5 𝒚 = 𝟒
Section 2 – Solve the simultaneous equations below
8.
2𝑥 + 3𝑦 = 11 𝒙 = 𝟏
2𝑥 + 4𝑦 = 17 𝒙 = 𝟏. 𝟓
3𝑥 + 5𝑦 = 18 𝒚 = 𝟑
6𝑥 − 2𝑦 = 2 𝒚 = 𝟑. 𝟓
10.
4𝑥 + 2𝑦 = 24 𝒙 = 𝟓
2𝑥 + 2𝑦 = 8 𝒙 = 𝟓
3𝑥 − 3𝑦 = 9 𝒚 = 𝟐
3𝑥 − 3𝑦 = 18 𝒚 = −𝟏
12.
2𝑥 + 3𝑦 = 5 𝒙 = −𝟐
3𝑥 + 5𝑦 = 15 𝒙 = −𝟐. 𝟓
7𝑥 + 4𝑦 = −2 𝒚 = 𝟑
5𝑥 + 3𝑦 = 1 𝒚 = 𝟒. 𝟓
Simultaneous Equations
1. Solve these simultaneous equations by subtracting your equations.
Remember to find both missing values
a) 5 p  5q  35
b) 9 x  6 y  39
c) 7 x  2 y  22
2 p  5q  26
5 x  6 y  35
5 x  2 y  14
2. Solve these simultaneous equations by adding your equations
a) 3a  4b  48
b) x  2 y  20
c) 5c  3d  3
7a  4b  32
9 x  2 y  80
7c  3d  39
3. Solve these simultaneous equations. Decide whether you should add
or subtract your equations.
a) 2 x  6 y  68
b) 7w  3z  58
c) 8 x  6 y  36
2 x  4 y  46
8 x  10 y  44
5w  3z  62
4. For these one or both equations may need to be multiplied first to
get equation where elimination can happen
a) 5 x  2 y  20
b) 3x  2 y  26
c) 2 x  9 y  69
2 x  4 y  24
4 x  y  20
x  3 y  24
d) 4 x  3 y  19
e) 5 x  2 y  61
3x  4 y  8
g) 3x  2 y  49
4x  3y  3
f)
6 x  2 y  16
5 x  5 y  10
2 x  5 y  22
h) 5 x  3 y  14
9 x  4 y  28
5. These are similar to Q4 but may need some rearrangement first to
ensure the x and y terms line up.
a)
6 x  52  2 y
5 x  7 y  70
b) 2m  9n  38
4m  6n  20
c)
4c  7  3d
5c  5d  15
ANSWERS TO Simultaneous Equations
1. Solve these simultaneous equations by subtracting your equations.
Remember to find both missing values
2. Solve these simultaneous equations by adding your equations