Answer to Question #86497 in Algebra for RAKESH DEY

Question

Solve the linear system
x+2y=4, 3x-y=2 by substitution.
If 4x+y=c, ax+by=3 is a system having the same solution set as previously equation find a,b,c.

Answer 1

x+2y=4, 3x-y=2. Solution:

Express y through x in first equation:

2y=4-x

y=(4-x)/2

Substitute y into the second equation:

3x-((4-x)/2)=2

multiply the whole equation by 2:

6x-(4-x)=4

6x-4+x=4

7x=0

x=0

Substitute x into the first equation:

0+2y=4

y=4/2

y=2

ANSWER:(0,2)

If 4x+y=c, ax+by=3 is a system having the same solution set as previously equation find a,b,c. Solution:

Substitute x,y, finding above, into equations:

4*0+2=c and a*0+b*2=3

c=2

a=arbitrary real number

b=3/2

With this a,b,c this system have same solution with system above