Is (4, 8) a solution to the following system of equations: 17x - 4y = 15 15x - 7y = 4
Understand the Problem
The question asks whether the point (4, 8) is a solution to the given system of linear equations. To determine this, we will substitute x = 4 and y = 8 into each equation and check if both equations are satisfied.
Answer
No
Answer for screen readers
No
Steps to Solve
- Substitute x = 4 and y = 8 into the first equation
Substitute $x = 4$ and $y = 8$ into the equation $17x - 4y = 15$:
$17(4) - 4(8) = 15$
- Simplify the first equation
Calculate the left-hand side of the equation:
$68 - 32 = 15$ $36 = 15$
Since $36 \ne 15$, the first equation is not satisfied.
- Check the second equation (optional, but demonstrates best practice)
Substitute $x = 4$ and $y = 8$ into the equation $15x - 7y = 4$:
$15(4) - 7(8) = 4$
- Simplify the second equation
Calculate the left-hand side of the equation:
$60 - 56 = 4$ $4 = 4$
The second equation is satisfied, but the first isn't.
- Determine if (4, 8) is a solution
For (4, 8) to be a solution, it must satisfy both equations. Since the first equation is not satisfied, (4, 8) is not a solution to the system of equations.
No
More Information
A solution to a system of equations must satisfy all equations in the system. If a point does not satisfy even one equation, it is not a solution to the system.
Tips
A common mistake is to only check one of the equations. A point must satisfy all equations in the system to be a valid solution. Another common mistake is to make arithmetic errors when substituting and simplifying.
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