What is the solution to the system of equations?
[tex]\begin{array}{l}
y=-5 x+3 \
y=1
\end{array}[/tex]
A. (0.4,1)
B. (0.8,1)
C. (1,0.4)
D. (1,0.8)
Answer (2)
The solution to the system of equations is (0.4, 1), confirmed by substituting the values back into both equations. Therefore, the correct multiple-choice option is A. (0.4, 1).
;
Substitute y = 1 into the first equation.
Solve for x : 1 = − 5 x + 3 ⇒ x = 5 2 = 0.4 .
The solution is ( x , y ) = ( 0.4 , 1 ) .
Verify the solution in both equations to ensure correctness. The final answer is ( 0.4 , 1 ) .
Explanation
Analyze the problem We are given a system of two equations:
y = − 5 x + 3 y = 1
We want to find the values of x and y that satisfy both equations.
Substitute the value of y Since we know that y = 1 , we can substitute this value into the first equation to solve for x :
1 = − 5 x + 3
Solve for x Now, we solve for x :
Subtract 3 from both sides: 1 − 3 = − 5 x + 3 − 3 − 2 = − 5 x
Divide both sides by -5: − 5 − 2 = x x = 5 2 x = 0.4
State the solution So, we have x = 0.4 and y = 1 . Therefore, the solution to the system of equations is ( 0.4 , 1 ) .
Verify the solution We can verify this solution by substituting x = 0.4 and y = 1 into both equations:
Equation 1: y = − 5 x + 3 1 = − 5 ( 0.4 ) + 3 1 = − 2 + 3 1 = 1 (Correct)
Equation 2: y = 1 (Correct)
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 = 2 x + 100 and its revenue function is y = 6 x , solving this system of equations will give the number of units the company needs to sell to break even. In this case, solving the system gives x = 25 and y = 150 , meaning the company breaks even when it sells 25 units and has a cost and revenue of $150.
