Question

Solve the following pair of linear equations:
$ax + bx = c \\ bx + ax = 1 + c$
​

Answer 1

Step-by-step explanation:

Step-by-step explanation:

Given system of equations:

ax+by=c ---(1)

bx+ay=1+c ----(2)

multiply equation (1) by a, and equation (2) by b , we get

a²x+aby=ac---(3)

b²x+aby=b+bc---(4)

Subtract (4) from (3) , we get

(a²-b²)x= ac-b-bc

Now,

multiply equation (1) by b, and equation (2) by a , we get

abx+b²y=bc---(5)

abx+a²y=a+ac---(6)

Subtract (5) from (6), we get

(a²-b²)y = a+ac-bc

hence proved.

Answer 2

Step-by-step explanation:

Solution: (i) x + y = 14 ; x – y = 4

solve first equation

x + y = 14

x = 14 - y …………..(1)

plug this value in equation second we get

x – y = 4

14 – y - y = 4

Add 14 both side we get

- 2 y = 4 - 14

- 2 y = - 10

Y = -10/-2

Y = 5

Plug y = 5 in equation first we get

X = 14 – y

X = 14 – 5

X = 9

Answer x = 9 , y = 5

(ii)s – t = 3 ; s/3 + t/2 = 6

Solve first equation

s – t = 3

s = 3+t …………(1)

Plug this value in equation second we get

s/3 + t/2 = 6

Multiply by 6 to remove all denominator we get

6 + 2t + 3t = 36

5t = 36 – 6

5t = 30

Divide by 2 we get

t = 30/5

t =6

Plug the value in equation first we get

s = 3 +6

s = 9

Answer s = 9 , t = 6