Answered

Join the growing community of curious minds on IDNLearn.com. Ask your questions and receive reliable, detailed answers from our dedicated community of experts.

To solve the system of linear equations [tex]3x + 5y = 2[/tex] and [tex]6x + 10y = 8[/tex] by using the linear combination method, Laura correctly multiplied the first equation by -2 to get [tex]-6x - 10y = -4[/tex] and then correctly added the equations [tex]-6x - 10y = -4[/tex] and [tex]6x + 10y = 8[/tex] to get [tex]0 = 4[/tex]. How many solutions are there to the system of equations?

A. 0
B. 1
C. 2
D. 4

Sagot :

GinnyAnsweridn
To solve the given system of equations using the linear combination (or addition) method, let's analyze the steps involved:

We start with the system of equations:
1. [tex]\( 3x + 5y = 2 \)[/tex]
2. [tex]\( 6x + 10y = 8 \)[/tex]

Laura correctly multiplies the first equation by -2:
[tex]\[ -2 \times (3x + 5y) = -2 \times 2 \][/tex]
This simplifies to:
[tex]\[ -6x - 10y = -4 \][/tex]

Next, she adds the modified first equation to the second equation:
[tex]\[ (-6x - 10y) + (6x + 10y) = -4 + 8 \][/tex]

Combining the left-hand side terms:
[tex]\[ -6x - 10y + 6x + 10y = 0 \][/tex]
This simplifies to:
[tex]\[ 0 = -4 + 8 \][/tex]

And combining the right-hand sides:
[tex]\[ 0 = 4 \][/tex]

The resulting equation [tex]\( 0 = 4 \)[/tex] is a contradiction, as [tex]\( 0 \)[/tex] cannot equal [tex]\( 4 \)[/tex].

Since we arrived at a contradiction, this means that the system of equations is inconsistent and has no solutions.

Thus, the number of solutions to the system of equations is:
[tex]\[ 0 \][/tex]
Thank you for using this platform to share and learn. Keep asking and answering. We appreciate every contribution you make. Find the answers you need at IDNLearn.com. Thanks for stopping by, and come back soon for more valuable insights.