Westonci.ca connects you with experts who provide insightful answers to your questions. Join us today and start learning! Experience the ease of finding precise answers to your questions from a knowledgeable community of experts. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.

Is [tex]\((-2, 6)\)[/tex] a solution to the system of linear equations [tex]\(x + 2y = 10\)[/tex] and [tex]\(3x + y = 0\)[/tex]?

A. Yes, because the graphs don't intersect at [tex]\((-2, 6)\)[/tex].
B. No, because the graphs don't intersect at [tex]\((-2, 6)\)[/tex].
C. No, because the graphs intersect at [tex]\((-2, 6)\)[/tex].
D. Yes, because the graphs intersect at [tex]\((-2, 6)\)[/tex].

Sagot :

To determine whether the point [tex]\((-2, 6)\)[/tex] is a solution to the system of linear equations:
1. [tex]\( x + 2y = 10 \)[/tex]
2. [tex]\( 3x + y = 0 \)[/tex]

we need to see if substituting [tex]\( x = -2 \)[/tex] and [tex]\( y = 6 \)[/tex] into both equations satisfies them.

### Checking the First Equation:
Substitute [tex]\( x = -2 \)[/tex] and [tex]\( y = 6 \)[/tex] into [tex]\( x + 2y = 10 \)[/tex]:
[tex]\[ -2 + 2(6) = -2 + 12 = 10 \][/tex]
This simplifies to:
[tex]\[ 10 = 10 \][/tex]
This is true, so the point [tex]\((-2, 6)\)[/tex] satisfies the first equation.

### Checking the Second Equation:
Substitute [tex]\( x = -2 \)[/tex] and [tex]\( y = 6 \)[/tex] into [tex]\( 3x + y = 0 \)[/tex]:
[tex]\[ 3(-2) + 6 = -6 + 6 = 0 \][/tex]
This simplifies to:
[tex]\[ 0 = 0 \][/tex]
This is also true, so the point [tex]\((-2, 6)\)[/tex] satisfies the second equation.

Since [tex]\((-2, 6)\)[/tex] satisfies both equations, it is indeed a solution to the system of linear equations.

Therefore, the correct answer is:
Yes, because the graphs intersect at [tex]\((-2, 6)\)[/tex].
We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.