Question

How to find the point of interception for
$8x - 5y = 11 \\ 4x - 3y = 5$
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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 $(x, y) :( 2,1)$