$2 x+y=8$ and $x-y=1$. Solve by substitution method.

To solve the equations 2 x + y = 8 and x − y = 1 using substitution, we found y = 2 and x = 3 . The solution is expressed as the ordered pair ( 3 , 2 ) .
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Answered by Anonymous | 2025-07-04

Solve the second equation for x : x = y + 1 .
Substitute x into the first equation: 2 ( y + 1 ) + y = 8 .
Solve for y : y = 2 .
Substitute y back to find x : x = 3 . The solution is ( 3 , 2 ) ​ .

Explanation

Analyze the problem We are given the following system of equations:

2 x + y = 8 x − y = 1
We need to solve this system using the substitution method.

Solve for x First, we solve the second equation for x in terms of y :

x − y = 1 x = y + 1

Substitute x into the first equation Now, we substitute the expression for x into the first equation:

2 x + y = 8 2 ( y + 1 ) + y = 8

Solve for y Next, we simplify and solve for y :

2 ( y + 1 ) + y = 8 2 y + 2 + y = 8 3 y + 2 = 8 3 y = 6 y = 2

Solve for x Now that we have the value of y , we can substitute it back into the expression for x :

x = y + 1 x = 2 + 1 x = 3

State the solution Therefore, the solution to the system of equations is x = 3 and y = 2 . We can write this as the ordered pair ( 3 , 2 ) .

Examples
Substitution method is a powerful tool in various real-life scenarios. For instance, consider a scenario where you're trying to optimize your study time between two subjects, Math and Science. If you know that each hour spent on Math improves your grade by a certain amount, and each hour on Science improves it by another amount, and you have a limited number of hours, you can use substitution to find the optimal allocation of your time to maximize your overall grade improvement. This method allows you to express one variable in terms of another, helping you make informed decisions to achieve the best outcome.

Answered by GinnyAnswer | 2025-07-04