Question

7. Solve the following pair of linear equations:

(ii) ax+by=c
bx + ay = 1+c
(v) 152x-378y=-74
-378x + 152y=-604
​

Answer 1

Answer:

(ii). ($\frac{ac-b-bc}{a^2- b^2}$ ,  $\frac{a+ac-bc}{a^2-b^2}$) , (v). (2, 1)

Step-by-step explanation:

ax + by = c ..... (1)

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

Let's use elimination method: multiply (1) by "a" and (2) by "-b" , then add both equations.

a²x + aby = ac

-b²x - aby = -b - bc

(a² - b²)x = ac - b - bc

x = $\frac{ac-b-bc}{a^2- b^2}$

Now let's multiply equation (1) by "-b", and equation (2) by "a" and add them, we get:

- abx - b²y = - bc

abx + a²y = a + ac

(a² - b²)y = a + ac - bc

y = $\frac{a+ac-bc}{a^2-b^2}$

(v). x = 2, y = 1 , I solved given system graphically.