Question

Find a if the line 3x + ay = 8, passes through the intersection of lines represented by
equations 3x – 2y = 10 and 5x + y = 8.​

Answer 1

Answer:

a=-1

Step-by-step explanation:

3x-2y=10_(1)

5x+y=8

y=8-5x

put the value of y in1 we get

x=2

y= -2

put the value of x and y in eq

3x+ay=8 we get

a=-1

Answer 2

The value of a is equal to -1.

Given in the question that the line 3x + ay = 8 passes through the point of intersection of the two lines 3x – 2y = 10 and 5x + y = 8 .

Solving the lines 3x – 2y = 10 and 5x + y = 8 for the point of intersection -

5x + y = 8

=> y = 8-5x

3x - 2y = 10

=> 3x - 2(8-5x) = 10 {y = 8-5x}

=> 3x - 16 + 10x = 10

=> 13x = 26

=> x = 2

y = -2

The line 3x + ay = 8 passes through the point (2,-2) and this point will satisfy the line-

=> 6 - 2a = 8

=> a = -1

The value of a which satisfies the equation is -1.