Is (2, 3) a solution to the system of equations: y = -3x - 2 y = 4x - 5
Understand the Problem
The question asks if the point (2, 3) is a solution to the given system of equations. To verify this, we need to substitute x = 2 and y = 3 into both equations and check if both equations hold true. If both equations are true, then (2, 3) is a solution; otherwise, it is not.
Answer
No
Answer for screen readers
No
Steps to Solve
- Substitute x = 2 and y = 3 into the first equation
Substitute $x = 2$ and $y = 3$ into the first equation $y = -3x - 2$:
$3 = -3(2) - 2$
- Simplify the first equation
Simplify the right side of the equation:
$3 = -6 - 2$
$3 = -8$
Since $3 \ne -8$, the first equation is not true.
- Substitute x = 2 and y = 3 into the second equation
Substitute $x = 2$ and $y = 3$ into the second equation $y = 4x - 5$:
$3 = 4(2) - 5$
- Simplify the second equation
Simplify the right side of the equation:
$3 = 8 - 5$
$3 = 3$
Since $3 = 3$, the second equation is true. However, for (2, 3) to be a solution to the system of equations, it must satisfy both equations.
- Determine if (2, 3) is a solution
Since the point (2, 3) does not satisfy both equations, it 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 simultaneously.
Tips
A common mistake is only checking one of the equations. To verify if a point is a solution to a system of equations, you must check ALL the equations in the system. Another common mistake is making arithmetic errors when substituting and simplifying.
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