Westonci.ca is the ultimate Q&A platform, offering detailed and reliable answers from a knowledgeable community. Get the answers you need quickly and accurately from a dedicated community of experts on our Q&A platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.
Sagot :
To determine which linear system has the solution [tex]\( x = 5 \)[/tex] and [tex]\( y = -4 \)[/tex], we need to substitute these values into each of the given systems and check if the equations are satisfied.
System a:
1. [tex]\( x + 3y = 12 \)[/tex]
2. [tex]\( 4x - 2y = -27 \)[/tex]
Substituting [tex]\( x = 5 \)[/tex] and [tex]\( y = -4 \)[/tex]:
1. [tex]\( 5 + 3(-4) \)[/tex]
[tex]\( = 5 - 12 \)[/tex]
[tex]\( = -7 \)[/tex]
This does not equal [tex]\(12\)[/tex], so system [tex]\(a\)[/tex] is not satisfied.
System b:
1. [tex]\( 2x + 3y = 5 \)[/tex]
2. [tex]\( 2x + 4y = 10 \)[/tex]
3. [tex]\( -2x + y = 11 \)[/tex]
Substituting [tex]\( x = 5 \)[/tex] and [tex]\( y = -4 \)[/tex]:
1. [tex]\( 2(5) + 3(-4) \)[/tex]
[tex]\( = 10 - 12 \)[/tex]
[tex]\( = -2 \)[/tex]
This does not equal [tex]\(5\)[/tex], so system [tex]\(b\)[/tex] is not satisfied.
System c:
1. [tex]\( x + 3y = 5 \)[/tex]
Substituting [tex]\( x = 5 \)[/tex] and [tex]\( y = -4 \)[/tex]:
1. [tex]\( 5 + 3(-4) \)[/tex]
[tex]\( = 5 - 12 \)[/tex]
[tex]\( = -7 \)[/tex]
This does not equal [tex]\(5\)[/tex], so system [tex]\(c\)[/tex] is not satisfied.
System d:
1. [tex]\( 3x + y = 11 \)[/tex]
2. [tex]\( -2x + 4y = -26 \)[/tex]
Substituting [tex]\( x = 5 \)[/tex] and [tex]\( y = -4 \)[/tex]:
1. [tex]\( 3(5) + (-4) \)[/tex]
[tex]\( = 15 - 4 \)[/tex]
[tex]\( = 11 \)[/tex] (matches the first equation)
2. [tex]\( -2(5) + 4(-4) \)[/tex]
[tex]\( = -10 - 16 \)[/tex]
[tex]\( = -26 \)[/tex] (matches the second equation)
Both equations are satisfied, so system [tex]\(d\)[/tex] is satisfied.
Therefore, the linear system that has the solution [tex]\( x = 5 \)[/tex] and [tex]\( y = -4 \)[/tex] is system (d):
[tex]\[ 3x + y = 11 \][/tex]
[tex]\[ -2x + 4y = -26 \][/tex]
System a:
1. [tex]\( x + 3y = 12 \)[/tex]
2. [tex]\( 4x - 2y = -27 \)[/tex]
Substituting [tex]\( x = 5 \)[/tex] and [tex]\( y = -4 \)[/tex]:
1. [tex]\( 5 + 3(-4) \)[/tex]
[tex]\( = 5 - 12 \)[/tex]
[tex]\( = -7 \)[/tex]
This does not equal [tex]\(12\)[/tex], so system [tex]\(a\)[/tex] is not satisfied.
System b:
1. [tex]\( 2x + 3y = 5 \)[/tex]
2. [tex]\( 2x + 4y = 10 \)[/tex]
3. [tex]\( -2x + y = 11 \)[/tex]
Substituting [tex]\( x = 5 \)[/tex] and [tex]\( y = -4 \)[/tex]:
1. [tex]\( 2(5) + 3(-4) \)[/tex]
[tex]\( = 10 - 12 \)[/tex]
[tex]\( = -2 \)[/tex]
This does not equal [tex]\(5\)[/tex], so system [tex]\(b\)[/tex] is not satisfied.
System c:
1. [tex]\( x + 3y = 5 \)[/tex]
Substituting [tex]\( x = 5 \)[/tex] and [tex]\( y = -4 \)[/tex]:
1. [tex]\( 5 + 3(-4) \)[/tex]
[tex]\( = 5 - 12 \)[/tex]
[tex]\( = -7 \)[/tex]
This does not equal [tex]\(5\)[/tex], so system [tex]\(c\)[/tex] is not satisfied.
System d:
1. [tex]\( 3x + y = 11 \)[/tex]
2. [tex]\( -2x + 4y = -26 \)[/tex]
Substituting [tex]\( x = 5 \)[/tex] and [tex]\( y = -4 \)[/tex]:
1. [tex]\( 3(5) + (-4) \)[/tex]
[tex]\( = 15 - 4 \)[/tex]
[tex]\( = 11 \)[/tex] (matches the first equation)
2. [tex]\( -2(5) + 4(-4) \)[/tex]
[tex]\( = -10 - 16 \)[/tex]
[tex]\( = -26 \)[/tex] (matches the second equation)
Both equations are satisfied, so system [tex]\(d\)[/tex] is satisfied.
Therefore, the linear system that has the solution [tex]\( x = 5 \)[/tex] and [tex]\( y = -4 \)[/tex] is system (d):
[tex]\[ 3x + y = 11 \][/tex]
[tex]\[ -2x + 4y = -26 \][/tex]
We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.