\begin{aligned} 3x-4y&=10 \\\\ 2x-4y&=6 \end{aligned}If satisfies the given system of equations, what is the value of ?

Eliminate y by subtraction: Subtract the second equation from the first to eliminate y: (3x - 4y) - (2x - 4y) = 10 - 6.Perform subtraction: Perform the subtraction: 3x - 2x = 10 - 6.Simplify to find x: Simplify the equation: x = 4.Check solution for x: Check the solution by plugging x = 4 into the original equations.Check solution for y: For the first equation: 3(4) - 4y = 10, which simplifies to 12 - 4y = 10.Verify correctness: For the second equation: 2(4) - 4y = 6, which simplifies to 8 - 4y = 6.Both equations should be true if x = 4 is the correct solution. Let's check if they give the same value for y.From the first equation, 12 - 4y = 10, we get 4y = 12 - 10, which simplifies to 4y = 2.From the second equation, 8 - 4y = 6, we get 4y = 8 - 6, which simplifies to 4y = 2.Both equations give 4y = 2, which means y = 2 / 4.Simplify y = 2 / 4 to get y = 0.5.Since both x = 4 and y = 0.5 satisfy the original equations, there is no math error, and the solution is correct.

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Q. \begin{aligned} 3x-4y&=10 \newline 2x-4y&=6 \end{aligned}If

x

satisfies the given system of equations, what is the value of

x

Eliminate y by subtraction: Subtract the second equation from the first to eliminate y: $(3x - 4y) - (2x - 4y) = 10 - 6$ .
Perform subtraction: Perform the subtraction: $3x - 2x = 10 - 6$ .
Simplify to find $x$ : Simplify the equation: $x = 4$ .
Check solution for $x$ : Check the solution by plugging $x = 4$ into the original equations.
Check solution for $y$ : For the first equation: $3(4) - 4y = 10$ , which simplifies to $12 - 4y = 10$ .
Verify correctness: For the second equation: $2(4) - 4y = 6$ , which simplifies to $8 - 4y = 6$ .
Verify correctness: For the second equation: $2(4) - 4y = 6$ , which simplifies to $8 - 4y = 6$ . Both equations should be true if $x = 4$ is the correct solution. Let's check if they give the same value for $y$ .
Verify correctness: For the second equation: $2(4) - 4y = 6$ , which simplifies to $8 - 4y = 6$ . Both equations should be true if $x = 4$ is the correct solution. Let's check if they give the same value for $y$ . From the first equation, $12 - 4y = 10$ , we get $4y = 12 - 10$ , which simplifies to $4y = 2$ .
Verify correctness: For the second equation: $2(4) - 4y = 6$ , which simplifies to $8 - 4y = 6$ . Both equations should be true if $x = 4$ is the correct solution. Let's check if they give the same value for $y$ . From the first equation, $12 - 4y = 10$ , we get $4y = 12 - 10$ , which simplifies to $4y = 2$ . From the second equation, $8 - 4y = 6$ , we get $4y = 8 - 6$ , which simplifies to $4y = 2$ .
Verify correctness: For the second equation: $2(4) - 4y = 6$ , which simplifies to $8 - 4y = 6$ . Both equations should be true if $x = 4$ is the correct solution. Let's check if they give the same value for $y$ . From the first equation, $12 - 4y = 10$ , we get $4y = 12 - 10$ , which simplifies to $4y = 2$ . From the second equation, $8 - 4y = 6$ , we get $4y = 8 - 6$ , which simplifies to $4y = 2$ . Both equations give $4y = 2$ , which means $8 - 4y = 6$ $1$ .
Verify correctness: For the second equation: $2(4) - 4y = 6$ , which simplifies to $8 - 4y = 6$ . Both equations should be true if $x = 4$ is the correct solution. Let's check if they give the same value for $y$ . From the first equation, $12 - 4y = 10$ , we get $4y = 12 - 10$ , which simplifies to $4y = 2$ . From the second equation, $8 - 4y = 6$ , we get $4y = 8 - 6$ , which simplifies to $4y = 2$ . Both equations give $4y = 2$ , which means $8 - 4y = 6$ $1$ . Simplify $8 - 4y = 6$ $1$ to get $8 - 4y = 6$ $3$ .
Verify correctness: For the second equation: $2(4) - 4y = 6$ , which simplifies to $8 - 4y = 6$ . Both equations should be true if $x = 4$ is the correct solution. Let's check if they give the same value for $y$ . From the first equation, $12 - 4y = 10$ , we get $4y = 12 - 10$ , which simplifies to $4y = 2$ . From the second equation, $8 - 4y = 6$ , we get $4y = 8 - 6$ , which simplifies to $4y = 2$ . Both equations give $4y = 2$ , which means $8 - 4y = 6$ $1$ . Simplify $8 - 4y = 6$ $1$ to get $8 - 4y = 6$ $3$ . Since both $x = 4$ and $8 - 4y = 6$ $3$ satisfy the original equations, there is no math error, and the solution is correct.