Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. x-3y= -14 4x+3y= 19
Linear equations are fundamental in mathematics and have a wide range of applications in various fields, including physics, engineering, and economics. When dealing with a system of linear equations, it’s important to determine whether the system has one and only one solution, infinitely many solutions, or no solution. In this essay, we will explore and analyze the given system of linear equations:
Our goal is to determine the nature of the solutions to this system.
To determine whether the system of linear equations has one solution, infinitely many solutions, or no solution, we can use several techniques, such as substitution, elimination, or graphing. In this case, we will use the elimination method to solve the system.
Step 1: Elimination We’ll begin by eliminating one of the variables by adding or subtracting the equations. In this case, we can eliminate the variable ‘y’ by adding the two equations together:
(x – 3y) + (4x + 3y) = (-14) + 19
This simplifies to:
5x = 5
Step 2: Solve for ‘x’ Now, we can solve for ‘x’ by dividing both sides of the equation by 5:
5x/5 = 5/5 x = 1
Step 3: Substitute ‘x’ back into one of the equations Let’s substitute the value of ‘x’ into the first equation to solve for ‘y’:
1 – 3y = -14
Step 4: Solve for ‘y’ Now, solve for ‘y’ by isolating it on one side of the equation:
-3y = -14 – 1 -3y = -15
Divide both sides by -3 to find the value of ‘y’:
y = 5
After applying the elimination method to the given system of linear equations, we found that ‘x’ equals 1, and ‘y’ equals 5. Therefore, the solution to this system of equations is:
x = 1 y = 5
This result indicates that the system has one and only one solution. In graphical terms, these two equations represent two lines that intersect at a single point (1, 5) on the coordinate plane, confirming the uniqueness of the solution.
In summary, the system of linear equations:
has one and only one solution, which is x = 1 and y = 5. This demonstrates the power of algebraic techniques in solving systems of linear equations and provides valuable insight into real-world problem-solving scenarios.
As a renowned provider of the best writing services, we have selected unique features which we offer to our customers as their guarantees that will make your user experience stress-free.
Unlike other companies, our money-back guarantee ensures the safety of our customers' money. For whatever reason, the customer may request a refund; our support team assesses the ground on which the refund is requested and processes it instantly. However, our customers are lucky as they have the least chances to experience this as we are always prepared to serve you with the best.
Plagiarism is the worst academic offense that is highly punishable by all educational institutions. It's for this reason that Peachy Tutors does not condone any plagiarism. We use advanced plagiarism detection software that ensures there are no chances of similarity on your papers.
Sometimes your professor may be a little bit stubborn and needs some changes made on your paper, or you might need some customization done. All at your service, we will work on your revision till you are satisfied with the quality of work. All for Free!
We take our client's confidentiality as our highest priority; thus, we never share our client's information with third parties. Our company uses the standard encryption technology to store data and only uses trusted payment gateways.
Anytime you order your paper with us, be assured of the paper quality. Our tutors are highly skilled in researching and writing quality content that is relevant to the paper instructions and presented professionally. This makes us the best in the industry as our tutors can handle any type of paper despite its complexity.
Recent Comments