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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 ?

3m=2(l4)m=l43 - m = 2(l-4) \newline m = l - 4 \newlineConsider the given system of equations. If (,m)(\ell,m) is the solution to the system, then what is the value of m\ell\cdot m?\newline\square

Full solution

Q. 3m=2(l4)m=l43 - m = 2(l-4) \newline m = l - 4 \newlineConsider the given system of equations. If (,m)(\ell,m) is the solution to the system, then what is the value of m\ell\cdot m?\newline\square
  1. Given Equations: We are given the system of equations:\newline11) 3m=2(4)3 - m = 2(\ell - 4)\newline22) m=4m = \ell - 4\newlineLet's solve the system using substitution or elimination. Since the second equation gives us mm directly in terms of \ell, we can substitute mm from the second equation into the first equation.
  2. Substitute mm: Substitute mm from the second equation into the first equation:\newline3(4)=2(4)3 - (\ell - 4) = 2(\ell - 4)\newlineNow, simplify the equation by distributing the negative sign and the 22 on the right side.
  3. Simplify Equation: Simplify the equation: \newline3+4=283 - \ell + 4 = 2\ell - 8\newlineNow, combine like terms on the left side.
  4. Combine Like Terms: Combine like terms:\newline7=287 - \ell = 2\ell - 8\newlineNow, add \ell to both sides to get all the \ell terms on one side.
  5. Add \ell: Add \ell to both sides:\newline7=387 = 3\ell - 8\newlineNow, add 88 to both sides to isolate the \ell term.
  6. Add 88: Add 88 to both sides:\newline15=315 = 3\ell\newlineNow, divide both sides by 33 to solve for \ell.
  7. Divide by 33: Divide both sides by 33:\newline=5\ell = 5\newlineNow that we have the value of \ell, we can substitute it back into the second equation to find mm.
  8. Substitute \ell: Substitute \ell into the second equation to find mm:m=54m = 5 - 4Now, simplify the right side.
  9. Simplify Right Side: Simplify the right side:\newlinem=1m = 1\newlineNow we have the values of \ell and mm. We can multiply them to find ×m\ell \times m.
  10. Multiply \ell and mm: Multiply \ell and mm to find m\ell\cdot m:m=51\ell\cdot m = 5 \cdot 1Now, calculate the product.
  11. Calculate Product: Calculate the product:\newlinem=5\ell\cdot m = 5\newlineWe have found the value of m\ell\cdot m.

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