$\begin{array}{l}M+3 N=5 \\ M-N=1 \\ M \times N=?\end{array}$
Answer (1)
Express M in terms of N using the second equation: M = N + 1 .
Substitute this expression into the first equation and solve for N : N = 1 .
Substitute the value of N back into the expression for M : M = 2 .
Calculate the product of M and N : 2 .
Explanation
Understanding the Problem We are given a system of two equations with two variables, M and N :
Equation 1: M + 3 N = 5 Equation 2: M − N = 1
Our goal is to find the product of M and N , which is M × N .
Expressing M in terms of N We can solve this system of equations using substitution or elimination. Let's use substitution. From Equation 2, we can express M in terms of N :
M = N + 1
Substituting into Equation 1 Now, substitute this expression for M into Equation 1:
( N + 1 ) + 3 N = 5
Solving for N Simplify and solve for N :
4 N + 1 = 5 4 N = 4 N = 1
Solving for M Substitute the value of N back into the equation M = N + 1 to find M :
M = 1 + 1 M = 2
Calculating M times N Now that we have the values of M and N , we can calculate their product:
M × N = 2 × 1 = 2
Final Answer Therefore, the product of M and N is 2.
Examples
Imagine you're baking cookies and need to adjust a recipe. If you know that the total amount of flour and sugar should be 5 cups, and the amount of flour should be 1 cup more than the amount of sugar, you can set up a system of equations similar to the one above. Solving this system will tell you exactly how much flour and sugar you need, ensuring your cookies turn out perfectly. This type of problem-solving is useful in many situations where you need to balance different quantities to achieve a desired outcome.
