In a system of equations, a is a constant and c and y are variables. For what va

pancha3

pancha3

Answered question

2021-09-10

In a system of equations, a is a constant and c and y are variables. For what value of a will be the system of equations have infinitely many solutions? 2x- 1/2y=15 ax-1/3y=10

Answer & Explanation

wheezym

wheezym

Skilled2021-09-11Added 103 answers

Step 1
Two linear equations ax1+by1+c1=0 and ax2+by2+c2=0 has infinitely many solutions if
a1a2=b1b2=c1c2
Consider the given equations are
2x12y=15...(i)
ax13y=10...(ii)
Multiply both sides by 2 in equation (i) and multiply both sides by 3 in equation (ii).
4x-y=30
3ax-y=30
These equations can be rewritten as
4x−y−30=0
3ax−y−30=0
Step 2
On comparing these equations with ax1+by1+c1=0 and ax2+by2+c2=0, we get
a1=4,b1=1,c1=30,a2=3a,b2=1,c2=30
The given equations have infinitely many solutions if
a1a2=b1b2=c1c2
On substituting the values, we get
43a=11=3030
43a=1=1
43a=1
43=a
Step 3
Answer: The given equations have infinitely many solutions for a=43.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?