Is (4, 2) a solution to the system of equations: 3x + 2y = 14 y = 2
Understand the Problem
The question asks us to verify whether the point (4, 2) is a solution to the given system of equations. To do this, we will plug in the values x = 4 and y = 2 into each equation and see if they hold true. If both equations are true for these values, then (4, 2) is a solution.
Answer
no
Answer for screen readers
no
Steps to Solve
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Substitute $x = 4$ and $y = 2$ into the first equation. Replace $x$ with 4 and $y$ with 2 in the equation $3x + 2y = 14$: $3(4) + 2(2) = 14$
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Simplify the left side. Perform the multiplication: $12 + 4 = 14$
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Check if the equation holds. Add the numbers on the left side: $16 = 14$ This statement is false.
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Check the second equation. Substitute $y = 2$ into the second equation $y = 2$: $2 = 2$ This statement is true.
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Determine if (4, 2) is a solution. Since the point (4, 2) does not satisfy the first equation, 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. In this case, while (4, 2) satisfies the second equation, it does not satisfy the first equation. Therefore, it is not a solution to the system.
Tips
A common mistake is to only check one of the equations. To be a solution to the system of equations, the point must satisfy all equations. Additionally, calculation errors can lead to an incorrect conclusion so it's good to double-check your arithmetic.
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