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

View step-by-step help

Home

Math Problems

Precalculus

Find values of derivatives using limits

Full solution

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.