Solve the system for $x$ and $y$.

$\begin{array}{l}
8 x-y=48 \
8 x-5 y=71
\end{array}$

To solve the given system of equations, we first eliminated x by subtracting the equations, which gave us y = − 5.75 . Then, substituting this value back into one of the original equations allowed us to find x = 5.28125 . Thus, the solution is ( 5.28125 , − 5.75 ) .
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Answered by Anonymous | 2025-07-04

( 5.28125 , − 5.75 ) ​

Explanation

Analyze the problem We are given a system of two linear equations:

8 x − y = 48 8 x − 5 y = 71
Our goal is to find the values of x and y that satisfy both equations. We will use the elimination method to solve this system.

Eliminate x and solve for y To eliminate x , we can subtract the first equation from the second equation:

( 8 x − 5 y ) − ( 8 x − y ) = 71 − 48
Simplifying this, we get:
8 x − 5 y − 8 x + y = 23 − 4 y = 23
Now, we can solve for y :
y = − 4 23 ​ = − 4 23 ​ = − 5.75

Substitute y and solve for x Now that we have the value of y , we can substitute it back into one of the original equations to solve for x . Let's use the first equation:

8 x − y = 48 8 x − ( − 5.75 ) = 48 8 x + 5.75 = 48 8 x = 48 − 5.75 8 x = 42.25
Now, we can solve for x :
x = 8 42.25 ​ = 5.28125

State the solution Therefore, the solution to the system of equations is:

x = 5.28125 y = − 5.75
So the solution is ( 5.28125 , − 5.75 ) .
Examples
Systems of equations are used in various real-life scenarios, such as determining the break-even point for a business, calculating the optimal mix of ingredients in a recipe, or modeling supply and demand in economics. Understanding how to solve systems of equations helps in making informed decisions in these situations. For example, if a company wants to know how many units they need to sell to cover their costs, they can set up a system of equations to model their revenue and expenses and solve for the break-even point.

Answered by GinnyAnswer | 2025-07-04