Is (7, 8) a solution to the following system of equations? y = 2x + 6 y = (1/7)x + 7
Understand the Problem
The question asks whether the point (7, 8) is a solution to the given system of equations. This means we need to substitute x=7 and y=8 into each equation and see if both equations are true. If both are true, then (7, 8) is a solution; otherwise, it is not.
Answer
No
Answer for screen readers
No
Steps to Solve
- Substitute x and y values into the first equation
Substitute $x = 7$ and $y = 8$ into the first equation $y = 2x + 6$: $8 = 2(7) + 6$
- Evaluate the first equation
Simplify the right side of the equation: $8 = 14 + 6$ $8 = 20$
Since $8 \neq 20$, the point (7, 8) is not a solution to the first equation.
- Conclusion
Since the point (7, 8) does not satisfy the first equation, it cannot be a solution to the system of equations. We do not need to check the second equation.
No
More Information
A solution to a system of equations must satisfy all equations in the system. Since (7, 8) does not satisfy the first equation, it is not a solution to the system.
Tips
A common mistake would be to only check one of the equations. To be a solution to the system, the point must satisfy both equations. Another mistake would be to make a calculation error when substituting and evaluating the equations.
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