Is (7, 6) a solution to the system of equations: 4x - 5y = 2 2x - 4y = -10
Understand the Problem
The question asks to determine whether the point (7, 6) is a solution to the given system of linear equations:
4x - 5y = 2 2x - 4y = -10
To do this, we need to substitute x = 7 and y = 6 into both equations and check if both equations hold true. If both equations are true, then (7, 6) is a solution. Otherwise, it is not.
Answer
No
Answer for screen readers
No
Steps to Solve
- Substitute x = 7 and y = 6 into the first equation
Substitute the values into the equation $4x - 5y = 2$:
$4(7) - 5(6) = 28 - 30 = -2$
- Check if the first equation holds true
Since $-2 \ne 2$, the first equation is not satisfied.
- Substitute x = 7 and y = 6 into the second equation
Substitute the values into the equation $2x - 4y = -10$:
$2(7) - 4(6) = 14 - 24 = -10$
- Check if the second equation holds true
Since $-10 = -10$, the second equation is satisfied.
- Determine if (7, 6) is a solution to the system
For (7, 6) to be a solution, both equations must be satisfied. Since the first equation is not satisfied, (7, 6) is not a solution to the system.
No
More Information
A solution to a system of equations must satisfy all equations in the system. If even one equation is not satisfied, the point is not a solution to the system.
Tips
A common mistake is to only check one of the equations or to make a calculation error.
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