$\begin{array}{l}
y=-5 x+30 \\ x=10
\end{array}$
What is the solution to the system of equations?
A. $(-20,10)$
B. $(10,-20)$
C. $(10,4)$
D. $(4,10)$
Answer (1)
Substitute x = 10 into the first equation.
Calculate y = − 5 ( 10 ) + 30 .
Simplify to find y = − 20 .
The solution to the system of equations is ( 10 , − 20 ) .
Explanation
Analyze the problem We are given a system of two equations:
Equation 1: y = − 5 x + 30 Equation 2: x = 10
Our goal is to find the values of x and y that satisfy both equations simultaneously.
Substitute x into Equation 1 Since we already know that x = 10 , we can substitute this value into Equation 1 to solve for y :
y = − 5 ( 10 ) + 30
Solve for y Now, we simplify the equation to find the value of y :
y = − 50 + 30 y = − 20
State the solution Therefore, the solution to the system of equations is x = 10 and y = − 20 . We can write this as an ordered pair ( 10 , − 20 ) .
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. For instance, if a company wants to know how many units of a product they need to sell to cover their costs, they can set up a system of equations to represent their revenue and expenses. By solving the system, they can find the break-even point, which is the number of units they need to sell to make a profit.
