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![{:[-x+3=y],[-6x+18=6y]:}
Which of the following accurately describes all solutions to the system of equations shown?
Choose 1 answer:
(A)
x=0 and
y=3
(B)
x=3 and
y=0
(C) There are infinite solutions to the system.
(D) There are no solutions to the system.](https://externalquestionsimg-a4fuc2b6e0gtdqge.z01.azurefd.net/external-question-images/images/images/ka/DigitalSAT/Medium%20Algebra/Solving%20systems%20of%20linear%20equations%20medium/Q-14.png)
Which of the following accurately describes all solutions to the system of equations shown?Choose answer:(A) and (B) and (C) There are infinite solutions to the system.(D) There are no solutions to the system.
Full solution
Q. Which of the following accurately describes all solutions to the system of equations shown?Choose answer:(A) and (B) and (C) There are infinite solutions to the system.(D) There are no solutions to the system.
- Write Equations: Let's start by writing down the system of equations:. . Our goal is to determine the relationship between and and see if there is one solution, no solution, or infinitely many solutions.
- Express in Terms of y: We can express the first equation in terms of y:This is a linear equation representing a line on a coordinate plane.
- Manipulate Second Equation: Now let's manipulate the second equation to see if it can be simplified to look like the first equation:Divide both sides by to simplify:This is another linear equation representing a line on a coordinate plane.
