Answer to Question #91443 in Algebra for Ra

Question

To solve the linear system:
x+2y=4, 3x-y=2 .......(1)
by substitution.
If 4x+y=c, ax+by=3 is a system having the same solution set as (1), find a,b,c.

Answer 1

Express x from the first equation of the system: x=4-2y and substitute it into the second one: 3*(4-2y)-y=2 =>

12-7y=2 => y=10/7; x=4-2y => x=4 - 20/7 =>x= 8/7;

Substitute these roots to find a,b and c:

4x+y=c=> 4*(8/7)+10/7=c => c=6;

ax+bx=3=> a*(8/7)+b*(10/7)=3 => 8a+10b=21 => b=2.1-0.8a; a is any real number.

Answer: x=8/7; y=10/7; c=6; b=2.1-0.8a; a is any rational number.