Solving Equations

Question 1

Question:   Which of the following equations have x=2, y=3 as solution ?
(a) 8x-y = 12 (b) 2x+3y = 10

Answer:    (a) Substitute x=2, y=3 in 8x-y=12
8(2)-3=12
16-3=12

x=2, y=3 is not a solution of 8x-y=12
(b) Substitute x=2, y=3 in 2x+3y=10
2(2)+3(3)=10
4+9=10

x=2, y=3 is not a solution of 2x+3y=10.

Question 2

Question:   Find the values of a so that x=1, y=2 is a solution of:
(a) 2x+ay=10 (b) ax+2y=6 (c) x+2y=a

Answer:    (a) 2x+ay=10, substitute x=1, y=2
2(1)+a(12) = 10
2+2a=10
2a=8
a=4
(b) ax+2y=6, substitute x=1, y=2
a(1)+2(2)=6
a+4=6
a=6-4
a=2
x+2y=a , substitute x=1, y=2
1+2(2)=a
1+4=a
a=5

Question 3

Question:   Solve the following equation:
7x+5=3x-25

Answer:   

Question 4

Question:   Solve the following equation:
5x-(3x-1)=x-4

Answer:    5x-(3x-1)=x-4
5x-3x+1=x-4
2x-x=-4-1
x=-5

Question 5

Question:   Solve the following equation:

Answer:   

Question 6

Question:   Solve the following equation:

Answer:   
5(2-9x) = 4(15-4x) (by cross multiplication)
10-45 x= 60-16x
-45x+16x=60-10
-29x=50

Question 7

Question:   Solve the following equation:

Answer:   
5(3x+5) = 2(2x-1) (by cross-multiplication)
15x-4x = -2-25
11x = -27

Question 8

Question:   Solve the following equation:

Answer:    2x-(1-2x) = 5-3(1+x)
2x-1+2x = 5-3-3x
4x+3x = 5-3+1
7x=3

Question 9

Question:   Solve the following equation:

Answer:   
4x + 7 = -3 (2x + 1) (By cross-multiplication)
4x+7=-6x-3
4x+6x=-3-7
10x=-10

x=-1

Question 10

Question:   Solve the following equation:

Answer:   






x=2