IDNLearn.com offers a unique blend of expert answers and community-driven insights. Our platform offers detailed and accurate responses from experts, helping you navigate any topic with confidence.
Sagot :
To determine the solution of the given system of equations:
[tex]\[ \begin{array}{l} 5x - 4y = 6 \\ -5x + 4y = -10 \end{array} \][/tex]
Let's follow a step-by-step approach:
1. Write down the system of linear equations:
[tex]\[ \begin{array}{l} 5x - 4y = 6 \quad \quad (1) \\ -5x + 4y = -10 \quad \quad (2) \end{array} \][/tex]
2. Add the equations to eliminate one of the variables:
By adding Equation (1) and Equation (2):
[tex]\[ (5x - 4y) + (-5x + 4y) = 6 + (-10) \][/tex]
[tex]\[ 0 = -4 \][/tex]
3. Analyze the result:
The resulting equation [tex]\(0 = -4\)[/tex] is a contradiction. This implies that the system of equations has no solution.
4. Conclusion:
Since the result we obtained is a contradiction, we conclude that the given system of equations has no solution.
This indicates that the lines represented by these equations are parallel and never intersect. Therefore, the correct answer is:
- no solution
[tex]\[ \begin{array}{l} 5x - 4y = 6 \\ -5x + 4y = -10 \end{array} \][/tex]
Let's follow a step-by-step approach:
1. Write down the system of linear equations:
[tex]\[ \begin{array}{l} 5x - 4y = 6 \quad \quad (1) \\ -5x + 4y = -10 \quad \quad (2) \end{array} \][/tex]
2. Add the equations to eliminate one of the variables:
By adding Equation (1) and Equation (2):
[tex]\[ (5x - 4y) + (-5x + 4y) = 6 + (-10) \][/tex]
[tex]\[ 0 = -4 \][/tex]
3. Analyze the result:
The resulting equation [tex]\(0 = -4\)[/tex] is a contradiction. This implies that the system of equations has no solution.
4. Conclusion:
Since the result we obtained is a contradiction, we conclude that the given system of equations has no solution.
This indicates that the lines represented by these equations are parallel and never intersect. Therefore, the correct answer is:
- no solution
We appreciate your contributions to this forum. Don't forget to check back for the latest answers. Keep asking, answering, and sharing useful information. Thank you for choosing IDNLearn.com. We’re committed to providing accurate answers, so visit us again soon.