These two lines don't have an intersection, so there is no solution. Whenever the lines are parallel, there is no solution. The coefficients of the variables are the same, so these lines have the same slope. They will never overlap since they have different y-intercepts.
We can graph the two equations to visualize this:. When two equations have the same slope but different y-axis, they are parallel. Since there are no intersection points, the system has no solutions. The graph will make parallel lines. The algebraic solution will give a false statement.
Algebra 1 Systems of Linear Equations. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.
Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney. Hanley Rd, Suite St. Louis, MO Subject optional. Email address: Your name:. Solve the rational equation:.
Possible Answers:. Correct answer: no solution. Explanation : With rational equations we must first note the domain, which is all real numbers except and.
Report an Error. Find the solution set:. Correct answer: None of the other answers. Explanation : Use the substitution method to solve for the solution set. How many solutions does the equation below have?
Possible Answers: One. Correct answer: No solutions. Explanation : When finding how many solutions an equation has you need to look at the constants and coefficients. The coefficients are the numbers alongside the variables. The constants are the numbers alone with no variables. Use distributive property on the right side first. Practice: Number of solutions to a system of equations algebraically. How many solutions does a system of linear equations have if there are at least two?
Number of solutions to system of equations review. Next lesson. A system of linear equations usually has a single solution, but sometimes it can have no solution parallel lines or infinite solutions same line.
What if she is 12? As you can see, picking random numbers is a very inefficient strategy! You can represent this situation algebraically, which provides another way to find the answer. Find the ages of Amanda and her dad. What is the problem asking? Assign a variable to the unknown. Solve the equation for the variable.
Do the answers make sense? Amanda is 22 years old, and her father is 44 years old. Consider that the rental fee for a landscaping machine includes a one-time fee plus an hourly fee. You could use algebra to create an expression that helps you determine the total cost for a variety of rental situations. An equation containing this expression would be useful for trying to stay within a fixed expense budget.
A landscaper wants to rent a tree stump grinder to prepare an area for a garden. Write an expression for the rental cost for any number of hours. The problem asks for an algebraic expression for the rental cost of the stump grinder for any number of hours. An expression will have terms, one of which will contain a variable, but it will not contain an equal sign. Look at the values in the problem:.
Think about what this means, and try to identify a pattern. Since multiplication is repeated addition, you could also represent it like this:. What information is important to finding an answer? What is the variable? What expression models this situation? Using the information provided in the problem, you were able to create a general expression for this relationship.
This means that you can find the rental cost of the machine for any number of hours! The machine cannot be rented for part of an hour. The landscaper can rent the machine for 5 hours. It is often helpful to follow a list of steps to organize and solve application problems. Solving Application Problems. Follow these steps to translate problem situations into algebraic equations you can solve.
Read and understand the problem. Determine the constants and variables in the problem. Write an equation to represent the problem. Write a sentence that answers the question in the application problem.
Gina has found a great price on paper towels. She wants to stock up on these for her cleaning business. Write an equation that Gina could use to solve this problem and show the solution. The problem asks for how many packages of paper towels Gina can purchase. What is the problem asking you? What are the constants? What equation represents this situation?
Solve for p. Check your solution. Substitute 48 in for p in your equation. Gina can purchase 48 packages of paper towels.
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