3-m=2(ℓ-4) m=ℓ-4 Consider the given system of equations. If (ℓ,m) is the solution to the system, then what is the value of ℓ*m ?

Equation 1: We are given a system of two equations: 1) 3 - m = 2(ℓ - 4) 2) m = ℓ - 4 We need to find the value of ℓ*m. Let's start by solving the second equation for m.Equation 2: From the second equation, we have: m = ℓ - 4 This gives us the value of m in terms of ℓ.Solving for m: Now, let's substitute the value of m from the second equation into the first equation: 3 - (ℓ - 4) = 2(ℓ - 4) This will allow us to solve for ℓ.Substituting m into Equation 1: Simplify the equation: 3 - ℓ + 4 = 2ℓ - 8 7 - ℓ = 2ℓ - 8 Now, let's move all the ℓ terms to one side and the constants to the other side.Simplifying the equation: Add ℓ to both sides and add 8 to both sides: 7 + 8 = 2ℓ + ℓ 15 = 3ℓ Now, divide both sides by 3 to solve for ℓ.Moving terms to one side: ℓ = 15 / 3 ℓ = 5 We have found the value of ℓ.Solving for ℓ: Now that we have ℓ, we can find m using the second equation: m = ℓ - 4 m = 5 - 4 m = 1 We have found the value of m.Finding m: Finally, we need to find the product of ℓ and m to answer the ℓ*m = 5 * 1 ℓ*m = 5 We have found the value of ℓ*m.

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3-m=2(ℓ-4)

m=ℓ-4
Consider the given system of equations. If
(ℓ,m) is the solution to the system, then what is the value of
ℓ*m ?

$\begin{array}{c} 3-m=2(\ell-4) \\ m=\ell-4 \end{array}$ $\newline$ Consider the given system of equations. If $(\ell, m)$ is the solution to the system, then what is the value of $\ell \cdot m$ ?

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Algebra 1

Unions and intersections of sets

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\begin{array}{c} 3-m=2(\ell-4) \\ m=\ell-4 \end{array}

\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

Given system of equations: We are given a system of two equations: $\newline$ $1$ ) $3 - m = 2(\ell - 4)$ $\newline$ $2$ ) $m = \ell - 4$ $\newline$ We need to find the value of $\ell*m$ . Let's start by solving the second equation for $m$ .
Equation $2$ : From the second equation, we have: $\newline$ $m = \ell - 4$ $\newline$ This gives us the value of $m$ in terms of $\ell$ .
Substituting second equation in first equation: Now, let's substitute the value of m from the second equation into the first equation: $\newline$ $3 - (\ell - 4) = 2(\ell - 4)$ $\newline$ This will allow us to solve for $\ell$ .
Combining like terms: Simplify the equation: $\newline$ $3 - \ell + 4 = 2\ell - 8$ $\newline$ $7 - \ell = 2\ell - 8$ $\newline$ Now, let's move all the $\ell$ terms to one side and the constants to the other side.
Isolating the variable $\ell$ : Add $\ell$ to both sides and add $8$ to both sides: $\newline$ $7 + 8 = 2\ell + \ell$ $\newline$ $15 = 3\ell$ $\newline$ Now, divide both sides by $3$ to solve for $\ell$ .
Solving for the value $\ell$ : $\ell = \frac{15}{3}$ $\newline$ $\ell = 5$ $\newline$ We have found the value of $\ell$ .
Solving for the value $m$ : Now that we have $\ell$ , we can find $m$ using the second equation: $\newline$ $m = \ell - 4$ $\newline$ $m = 5 - 4$ $\newline$ $m = 1$ $\newline$ We have found the value of $m$ .
Finding the value of $\ell\cdot m$ : Finally, we need to find the product of $\ell$ and $m$ . $\newline$ $\ell\cdot m = 5 \cdot 1$ $\newline$ $\ell\cdot m = 5$ $\newline$ We have found that the value of $\ell\cdot m$ is $5$ .