Question

For what value of 2x-3y=7. (a+b) x-(a+b-3)y=4a+b has infinite pair of solution

Answer 1

By comparing both the equations with standard linear equation

(ax + by + c = 0)

We get;

• a1=2
• a2=(a+b)
• b1=-3
• b2=-(a+b-3)
• c1=7
• c2=(4a+b)

Since the equation has infinite solutions

Therefore;

$\frac{ a_{1} }{ a_{2}} \: = \frac{ b_{1} }{ b_{2}} \: = \frac{ c_{1} }{ c_{2}} \:$

$thus \\ \frac{2}{a + b} = \frac{7}{4a + b} \\ 8a + 2b \: = 7a + 7b \\ a = 5b.............(1)$

$thus \: \\ \frac{ - 3}{ - (a + b - 3)} = \frac{2}{a + b} \\ \frac{3}{a + b - 3} = \frac{2}{a + b} \\ \\ 3a + 3b = 2a + 2b - 6 \\ a + b \: = - 6.........(2)$

From (1) & (2);

• a + b = -6
• 5b + b = -6
• 6b = -6
• b = (-1)

From substituting value of b in (1);

• a = 5b
• a = 5(-1)
• a= (-5)

#answerwithquality

#BAL