Simultaneous Linear Equations (Other Methods)
Y10
Elimination after Rearranging
Rearrange these equations then solve using elimination.
1).
3x + y = 5
2).
4x = 2 + y
8x = 8 - 3y 3).
5x = 5 + 3y
3y = 4x + 5 4).
4x + 5y = 19
2x = y + 1
5x + y = 13
5).
3x = 1 + y
6).
5x - y = 3
x = 2y + 7
7).
x - 6y = 3
5x = 17 - 4y 8).
2x + 4y = 8
9x = -3y
5x + 3y + 4 = 0
9).
9x + 3y = 19 10).
6x = 11 + 3y
2x + y + 2 = 0 11).
7x + y - 3 = 0
3y = 10 + 4x 12).
4x = 2y - 8
7x = 2y + 6
10x - 2y = 9
13).
4x + y = 21 14).
3x = 12 + 3y
8 = 4x + 2y 15).
x = 2 - 3y 7y = 13 - 6x 16).
3x = 2y + 1
2x - 6 = y
4x = 22 - 3y
17).
10y + 26 = 3x 18).
6 - 5x = 2y
3y = 27 - 8x 19).
2x = 5y + 1
5x = 6 + 6y 20).
2 + 2y = 10x
4y + 3 = 5x
7x - 2y = 6
21).
10 - 2a = 4b 22).
7b + 3a = 16
3 + 2u = 10v 23).
4v + 3u - 5 = 0
5q = 12 - 3p 24).
4p = 6q - 22
7f = 9 - 4g
3g = 6 - 5f
25).
3y - 15 = 6x 26).
2x = 7 - 2y
2x = 3 + 6y 27).
6y = 2 - 8x
9x + 4 = -12y 28).
3x = 12y + 12
4x = 10 - 2y
x = 8 - 2y
29).
11t = 9 + 3s 30).
7t + 6 = -2s
6m = 1 - 2n 31).
9m - 6 = 6n
3i = 5 + 8h 32).
5i - 9 = 12h
8y = 7 - 4z
6y - 41 = 8z
Substitution
A).
Solve the following equations by substituting one equation into the other.
1).
y = 2x + 7
2).
y = 3x + 3
y = 4x + 3
3).
y = 2x + 11
y = 5x - 3
y = 3x + 7
4).
y = 4x + 9
5).
y = 7x - 6
y = 4x + 5
6).
y = x + 20
y = 6x - 1
y = 4x + 15
y = x - 2
y = 1/3 x + 3
y = 3/4 x - 3
7).
8).
9).
y = 1/2 x + 4
y = 2/3 x - 4
y = 1/4 x + 5
y = 4 - 1/2 x
y = 5 - 2/3 x
y = 7 - 3/5 x
10).
11).
12).
y = 1/2 x + 2
y = 4 - 1/3 x
y = 12 - 4/5 x
u = t - 5
b = 3/5 a + 19
q=p-4
13).
14).
u = 1/3 t + 7
15).
b = a + 1
q = 2/7 p + 31
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B).
Y10
Solve the following equations by substituting one equation into the other.
1).
y = x + 2
2).
2x + 3y = 26
y = x + 1
3).
2x + 2y = 26
x=y-3
2x + 3y = 24
4).
x = 2y - 1
5).
3x + y = 11
y = 2x - 1
6).
8x + 3y = 11
x = 8 - 5y
3x + 2y = 11
7).
y = 6 - 2x
8).
4x + 3y = 22
x = 6 - 8y
9).
3x + 6y = 9
x = 5 + 7y
2x - 4y = 15
10).
3x + 2y = 9
11).
y = 4 - 2x
6x - 3y = 39
12).
x = y + 7
2x + y = -13
x = 2y + 1
13).
y = 8 - 2x
14).
3x - 2y = 5
3x - 2y = 7
15).
y = 14 - 2x
3n - 4m = 7
m = 45 - 2n
16).
a = 3b - 12
17).
2b - 5a = 8
x = 6y - 2
18).
8y - 3x = 1
t = 1 - 7s
5s - 3t = 10
C).
Rearrange, then solve the following equations by substituting one equation into the other.
1).
x - y = 1
2).
x + y = 3
2x - y = 4
3).
3x + y = 11
2x - y = 5
4).
x + y = 4
3x - y = 1
x+y=3
5).
x - 3y = 6
6).
x + 3y = 0
x + 2y = 3
7).
2x + y = 0
x + y = 1
8).
3x - 2y = 8
3x - 4y = 1
y - 2x = 1
9).
m + 3n = 7 10).
4m - 2n = 7
a + b = 3
11).
5a - 5b = 1
3p + 7q = 11 12).
p - q = -4
2d + e = -8
6d - 2e = -27
Trial and Improvement
Solve the following simultaneous equations by trying different values.
1).
u + v = 7
2).
u - v = 1
a + b = 7
3).
a - b = 3
m + n = 5
4).
m - n = 3
p+q=9
p-q=5
5).
a + b = 4
6).
a - b = 4
u + v = 12
7).
u - v = 6
c + d = 9
8).
c - d = 7
h + i = 11
h-i=7
r + s = 3 1/2
p + q = 6 1/3
u + v = 5 1/4
m+n=7
9).
10).
11).
12).
r - s = 1/2
p - q = 2 1/3
u - v = 3/4
m-n=2
13).
p + q = 2
14).
p - q = 4
c + d = 3
15).
c - d = 7
h + i = -3
16).
h - i = -7
g + h = -2
g-h=0
u + v = -8
m + n = -6
r + s = 1/2
a + b = -1
17).
18).
u - v = 2
19).
m - n = 6
20).
r - s = 2 1/2
a - b = 3 2/3
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