Solve the system of equations.
[tex]
\begin{array}{l}
y=-5 x-8 \\
y=4 x+1
\end{array}
[/tex]

a. (1,-3)
b. (-1,-3)
c. (3,1)
d. No solution

Set the two equations equal to each other: − 5 x − 8 = 4 x + 1 .
Solve for x : x = − 1 .
Substitute the value of x into one of the original equations to solve for y : y = − 3 .
The solution to the system of equations is ( − 1 , − 3 ) ​ .

Explanation

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

y = − 5 x − 8 y = 4 x + 1
Our goal is to find the values of x and y that satisfy both equations.

Set the equations equal Since both equations are equal to y , we can set them equal to each other:

− 5 x − 8 = 4 x + 1

Solve for x Now, we solve for x . Add 5 x to both sides:

− 8 = 9 x + 1
Subtract 1 from both sides:
− 9 = 9 x
Divide both sides by 9:
x = − 1

Solve for y Now that we have the value of x , we can substitute it into either equation to find the value of y . Let's use the first equation:

y = − 5 ( − 1 ) − 8 y = 5 − 8 y = − 3

State the solution So the solution to the system of equations is x = − 1 and y = − 3 . Therefore, the solution is ( − 1 , − 3 ) .

Examples
Systems of equations are used in many real-world applications, such as determining the break-even point for a business. For example, if a company's cost function is y = 5 x + 1000 and its revenue function is y = 15 x , solving this system of equations will give the number of units the company needs to sell to break even. Another application is in physics, where systems of equations can be used to solve for unknown forces or velocities in a system.

Answered by GinnyAnswer | 2025-07-05