Question

The equation Ax+By=10 goes through the coordinates (6,5) and (-2,-5).What are the values of A and B

Answer 1

Given:

The equation $Ax+By=10$ goes through the coordinates (6,5) and (-2,-5).

To find:

The values of A and B.

Solution:

We have,

$Ax+By=10$

It goes through the coordinates (6,5) and (-2,-5). It means these points will satisfy the equation.

$A(6)+B(5)=10$

$6A+5B=10$       ...(i)

$A(-2)+B(-5)=10$

$-2A-5B=10$       ...(ii)

Adding (i) and (ii), we get

$(6A+5B)+(-2A-5B)=10+10$

$4A=20$

Divide both sides by 4.

$A=5$

Put A=5 in (i), we get

$6(5)+5B=10$

$30+5B=10$

$5B=10-30$

$5B=-20$

Divide both sides by 5.

$B=-4$

Therefore, the values of A and B are 5 and -4 respectively.