$3 - m = 2(l-4) \newline m = l - 4$ $\newline$ Consider the given system of equations. If $(\ell,m)$ is the solution to the system, then what is the value of $\ell\cdot m$ ? $\newline$ $\square$

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Simplify radical expressions with variables

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3 - m = 2(l-4) \newline m = l - 4

\newline

Consider the given system of equations. If

(\ell,m)

is the solution to the system, then what is the value of

\ell\cdot m

\newline

\square

Given Equations: We are given the system of equations: $\newline$ $1$ ) $3 - m = 2(\ell - 4)$ $\newline$ $2$ ) $m = \ell - 4$ $\newline$ Let's solve the system using substitution or elimination. Since the second equation gives us $m$ directly in terms of $\ell$ , we can substitute $m$ from the second equation into the first equation.
Substitute $m$ : Substitute $m$ from the second equation into the first equation: $\newline$ $3 - (\ell - 4) = 2(\ell - 4)$ $\newline$ Now, simplify the equation by distributing the negative sign and the $2$ on the right side.
Simplify Equation: Simplify the equation: $\newline$ $3 - \ell + 4 = 2\ell - 8$ $\newline$ Now, combine like terms on the left side.
Combine Like Terms: Combine like terms: $\newline$ $7 - \ell = 2\ell - 8$ $\newline$ Now, add $\ell$ to both sides to get all the $\ell$ terms on one side.
Add $\ell$ : Add $\ell$ to both sides: $\newline$ $7 = 3\ell - 8$ $\newline$ Now, add $8$ to both sides to isolate the $\ell$ term.
Add $8$ : Add $8$ to both sides: $\newline$ $15 = 3\ell$ $\newline$ Now, divide both sides by $3$ to solve for $\ell$ .
Divide by $3$ : Divide both sides by $3$ : $\newline$ $\ell = 5$ $\newline$ Now that we have the value of $\ell$ , we can substitute it back into the second equation to find $m$ .
Substitute $\ell$ : Substitute $\ell$ into the second equation to find $m$ : $m = 5 - 4$ Now, simplify the right side.
Simplify Right Side: Simplify the right side: $\newline$ $m = 1$ $\newline$ Now we have the values of $\ell$ and $m$ . We can multiply them to find $\ell \times m$ .
Multiply $\ell$ and $m$ : Multiply $\ell$ and $m$ to find $\ell\cdot m$ : $\ell\cdot m = 5 \cdot 1$ Now, calculate the product.
Calculate Product: Calculate the product: $\newline$ $\ell\cdot m = 5$ $\newline$ We have found the value of $\ell\cdot m$ .