Solve the system of equations:
[tex]
\begin{array}{l}
y=7 x-9 \
y=7 x+7
\end{array}
[/tex]
a. $(-4,1)$
b. $(-4,-1)$
c. $(4,1)$
d. No solution
Answer (2)
Set the two equations equal to each other: 7 x − 9 = 7 x + 7 .
Simplify the equation by subtracting 7 x from both sides: − 9 = 7 .
Recognize that the equation − 9 = 7 is a contradiction.
Conclude that the system of equations has No solution .
Explanation
Analyze the problem We are given a system of two linear equations:
y = 7 x − 9
y = 7 x + 7
We want to find the values of x and y that satisfy both equations simultaneously.
Set the equations equal Since both equations are solved for y , we can set them equal to each other:
7 x − 9 = 7 x + 7
Solve for x Now, let's solve for x . Subtract 7 x from both sides of the equation:
7 x − 9 − 7 x = 7 x + 7 − 7 x
− 9 = 7
Conclusion The equation − 9 = 7 is a contradiction, which means there is no value of x that can satisfy this equation. Therefore, the system of equations has no solution.
Examples
Systems of equations are used in various real-world applications, such as determining the break-even point for a business, modeling supply and demand in economics, and solving network flow problems. In this case, the system has no solution, which could represent a situation where two business models with different cost structures will never have the same profit at any level of sales.
The system of equations has no solution because the equations represent parallel lines that do not intersect. Hence, they cannot have a common x and y value. The chosen answer is 'No solution'.
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