Q. 3−m=2(l−4)m=l−4Consider the given system of equations. If (ℓ,m) is the solution to the system, then what is the value of ℓ⋅m?□
Given Equations: We are given the system of equations:1) 3−m=2(ℓ−4)2) m=ℓ−4Let's solve the system using substitution or elimination. Since the second equation gives us m directly in terms of ℓ, we can substitute m from the second equation into the first equation.
Substitute m: Substitute m from the second equation into the first equation:3−(ℓ−4)=2(ℓ−4)Now, simplify the equation by distributing the negative sign and the 2 on the right side.
Simplify Equation: Simplify the equation: 3−ℓ+4=2ℓ−8Now, combine like terms on the left side.
Combine Like Terms: Combine like terms:7−ℓ=2ℓ−8Now, add ℓ to both sides to get all the ℓ terms on one side.
Add ℓ: Add ℓ to both sides:7=3ℓ−8Now, add 8 to both sides to isolate the ℓ term.
Add 8: Add 8 to both sides:15=3ℓNow, divide both sides by 3 to solve for ℓ.
Divide by 3: Divide both sides by 3:ℓ=5Now that we have the value of ℓ, we can substitute it back into the second equation to find m.
Substitute ℓ: Substitute ℓ into the second equation to find m:m=5−4Now, simplify the right side.
Simplify Right Side: Simplify the right side:m=1Now we have the values of ℓ and m. We can multiply them to find ℓ×m.
Multiply ℓ and m: Multiply ℓ and m to find ℓ⋅m:ℓ⋅m=5⋅1Now, calculate the product.
Calculate Product: Calculate the product:ℓ⋅m=5We have found the value of ℓ⋅m.
More problems from Simplify radical expressions with variables