Question

Find the point 3x - 7x₂ =5. of the lines x, - 5x2 = 1 and of intersection

Answer 1

(
`(9)/(4),(1)/(4))`

Explanation:

We are given that two lines

`x_1-7x_2=5` and
`x_1-5x_2=1`

We have to find the intersection point of two lines

Let
`3x_1-7x_2=5` (equation 1)

`x_1-5x_2=1` (Equation 2)

Multiply equation 2 by 3 then subtract from equation 1

`-7x_2+15x_2=5-3`

`8x_2=2`

`x_2=(2)/(8)=(1)/(4)`

Substitute
`x_2=(1)/(4)` in the equation 1

Then, we get

`3x_1-7(1)/(4)=5`

`3x_1-(7)/(4)=5`

`3x_1=5+(7)/(4)=(20+7)/(4)=(27)/(4)`

`x_1=(27)/(4* 3)=(9)/(4)`

Hence, the intersection point of two given lines is (
`(9)/(4),(1)/(4))`