Question

How to find the point of interception for

`8x - 5y = 11 \\ 4x - 3y = 5`
​

Answer 1

For this case we have the following system of equations:

`8x-5y = 11\\4x-3y = 5`

We multiply the second equation by -2:

`-8x + 6y = -10`

Then we have the following equivalent system:

`8x-5y = 11\\-8x + 6y = -10`

We add the equations:

`8x-8x-5y + 6y = 11-10\\y = 1`

Thus, the value of the variable y is 1.

We look for the value of the variable x:

`8x-5 (1) = 11\\8x-5 = 11\\8x = 11 + 5\\8x = 16\\x = \frac {16} {8}\\x = 2`

Thus, the value of the variable x is 2.

Then the point of intersection of the equations is in
`(x, y) :( 2,1)`

Answer:

The point of intersection of the equations is in
`(x, y) :( 2,1)`