Westonci.ca connects you with experts who provide insightful answers to your questions. Join us today and start learning! Our platform offers a seamless experience for finding reliable answers from a network of experienced professionals. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.
Sagot :
To find the value of [tex]\( Q \)[/tex] in the given system of equations so that the solutions to the system are consistent, let's analyze the equations step-by-step.
We start with the system of equations:
[tex]\[ \begin{array}{l} x - 3y = 4 \quad \text{(1)} \\ 2x - 6y = Q \quad \text{(2)} \end{array} \][/tex]
We need to determine the value of [tex]\( Q \)[/tex] such that every solution [tex]\((x, y)\)[/tex] to equation (1) is also a solution to equation (2).
First, consider equation (1):
[tex]\[ x - 3y = 4 \][/tex]
We aim to see if this equation can help us determine what [tex]\( Q \)[/tex] must be.
Notice that equation (2) can be seen as a multiple of equation (1). To see this, let's multiply the entire equation (1) by 2:
[tex]\[ 2(x - 3y) = 2 \times 4 \][/tex]
That simplifies to:
[tex]\[ 2x - 6y = 8 \][/tex]
Now, compare this result with equation (2):
[tex]\[ 2x - 6y = Q \][/tex]
[tex]\[ 2x - 6y = 8 \][/tex]
From comparison, it is clear that for the two equations to be equivalent, [tex]\( Q \)[/tex] must be equal to 8.
Therefore, the value of [tex]\( Q \)[/tex] that makes the system consistent and ensures that the solution to the system is [tex]\(\{(x, y): x - 3y = 4\}\)[/tex] is:
[tex]\[ \boxed{8} \][/tex]
We start with the system of equations:
[tex]\[ \begin{array}{l} x - 3y = 4 \quad \text{(1)} \\ 2x - 6y = Q \quad \text{(2)} \end{array} \][/tex]
We need to determine the value of [tex]\( Q \)[/tex] such that every solution [tex]\((x, y)\)[/tex] to equation (1) is also a solution to equation (2).
First, consider equation (1):
[tex]\[ x - 3y = 4 \][/tex]
We aim to see if this equation can help us determine what [tex]\( Q \)[/tex] must be.
Notice that equation (2) can be seen as a multiple of equation (1). To see this, let's multiply the entire equation (1) by 2:
[tex]\[ 2(x - 3y) = 2 \times 4 \][/tex]
That simplifies to:
[tex]\[ 2x - 6y = 8 \][/tex]
Now, compare this result with equation (2):
[tex]\[ 2x - 6y = Q \][/tex]
[tex]\[ 2x - 6y = 8 \][/tex]
From comparison, it is clear that for the two equations to be equivalent, [tex]\( Q \)[/tex] must be equal to 8.
Therefore, the value of [tex]\( Q \)[/tex] that makes the system consistent and ensures that the solution to the system is [tex]\(\{(x, y): x - 3y = 4\}\)[/tex] is:
[tex]\[ \boxed{8} \][/tex]
Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.