Linear and Simultaneous Equations

71.
Solve the equation: y+15=2
y = ......................... [2]
Paper 1
72.
(a) Solve: 3w−13=8
......................... [2]
(b) Solve: 2x−13−x−22=1
......................... [3]
Paper 1
73.
(a) Simplify: a2×a−3−a0
(b) T=6km−n
(i) Find T when m=17, n=8 and k=13.
(ii) Make m the subject of the formula.
(c) Find x and y if y=x+43 and y=2x+14
(a) ......................... [2] (b)(i) T = ......................... [2] (b)(ii) m = ......................... [2] (c) x = ......................... y = ......................... [3]
Paper 1
74.
t varies inversely as the difference of r2 and 7.
t=9 when r=−2
(a) Write an equation for t, in terms of r.
......................... [2]
(b) It is further given that t=12 when r=ab, where a and b are integers. Find the value of a and the value of b.
......................... [2]
Paper 1
75.
Express as a single fraction in its lowest terms:
2x−35+x+13
................................. [3]
Paper 1
76.
(a) Solve: 3x+3=24
......................... [2]
(b) Solve the simultaneous equations:
2p+3q=21
3p−2q=−1
......................... [2]
(c) Solve: (2t−5)(t+3)=0
......................... [3]
Paper 1
77.
(a) Simplify: (m−2)2+(m2−3)
......................... [2]
(b) Simplify: x−12−34
......................... [2]
Paper 1
78.
(a) Given that 3x−5y=9, work out the value of 12x−20y.
......................... [2]
(b) Solve: x2−4x=21
......................... [2]
(c) Make t the subject of the formula: P=t3R
......................... [2]
Paper 1
79.
Express x−13−2x−12 as a single fraction. Write your answer as simply as possible.
................................. [3]
Paper 1
80.
Solve: 4−x=x−4
x = ......................... [2]
Paper 1
81.
(a) Given that a=b2+4c3, calculate the value of a when b=9 and c=11.
......................... [2]
(b) Given that x=b2+4ac, make a the subject of the formula.
......................... [2]
Paper 1
82.
Solve the simultaneous equations:
x+y=7
5x+2y=20
x = ......................... y = ......................... [4]
Paper 1
83.
Simplify:
(a) x−13+x+12

......................... [2]
(b) Solve the simultaneous equations:
3x+2y=9
2x−4y=22
......................... [3]
Paper 1
84.
Solve the simultaneous equations:
2p+3q=21
3p−2q=−1
p = ......................... q = ......................... [3]
Paper 1
85.
Solve the equation: 3a−12=a−2
a = ......................... [2]
Paper 1
86.
F=t+13
(a) Find F when t=−4
......................... [2]
(b) Make t the subject of the formula.
......................... [2]
Paper 1
87.
Factorise fully: 1−p2
................................. [2]
Paper 1
88.
(a) Solve: 3x+1=7
......................... [2]
(b) Solve the simultaneous equations:
2x−y=5
3x+2y=4
......................... [3]
Paper 1
33.
Solve:
x + 1.5 = 2.5 y
2 y − x = 0
x = ......................... y = ......................... [3]
Paper 3
34.
P = m 2 2 − x
(i) Find the value of P when m = 8, and x = −4.
......................... [2]
(ii) Make x the subject of the formula.
......................... [2]
(b) Solve the simultaneous equations.
......................... [3]
Paper 3
35.
Solve the simultaneous equations.
3 x + 2 y = 7
x − 2 y = − 3
x = ......................... y = ......................... [3]
Paper 3
36.
(a) Make y the subject of the formula: x = c y − 5
......................... [2]
(b) 3 x − 3 = 5 x − 7
......................... [2]
Paper 3
37.
Solve the simultaneous equations.
y + x = 10
x 2 + 4 = y + 6
x = ......................... y = ......................... [3]
Paper 3
38.
Solve the simultaneous equations.
3 x + 5 y = 19
4 x − 2 y = − 18
x = ......................... y = ......................... [3]
Paper 3
39.
Solve the simultaneous equations.
6 x − 2 y = 33
4 x − 3 y = 9
x = ......................... y = ......................... [4]
Paper 3
40.
When 2 y + 11 = 17 , work out the value of y. Show your working.
y = ......................... [2]
Paper 3
41.
Solve the equation 9 y + 3 = 5 y + 13 . Show your working.
y = ......................... [2]
Paper 3
42.
x + 1.5 x

The width of a rectangle is x cm.
The length is 15 cm more than the width.
The perimeter of the rectangle is 17 cm.

Write down an equation satisfied by x and solve it to find x.
x = ......................... [3]
Paper 3