(a)
To find:
A system of equations in the variables
Answer to Problem 1CC
A system of equations in variables
Explanation of Solution
Calculation:
A system of equations contains the same variables in a set of equation. In the system of linear equation, each equation is linear.
A system of linear equation with a variable
Here,
Conclusion:
A system of equations in variables
(b)
To find:
Three methods to solve a system of equations.
Answer to Problem 1CC
Three methods to solve a system of linear equations are substitution method, elimination method and graphical method.
Explanation of Solution
Calculation:
To solve a system of linear equation three methods are used as,
Substitution method:
To solve a system of linear equation with two variable, first obtain the value of one variable in terms of second variable and then substitute it into any of the two linear equations and obtain the equation in one variable and obtain the solution.
Back substitute the solution of variable that obtained into any of the two linear equations and obtain the solution of second variable.
Elimination method:
To solve a system of linear equation with two variables by elimination method, first multiply the equation with appropriate constants to make equal coefficient for same variable.
Add or subtract the equation and obtain the equation in one variable and get the solution of that variable.
Back substitute the solution of variable that obtained into any of the two linear equations and obtain the solution of second variable.
Graphical method:
To obtain the solution of two equations with two variables by graphical method, first sketch the graph of two equations in a common screen and obtain the intersection point of the equations.
The x -coordinate and y -coordinate of intersection point of the two equations gives the solution of the linear equations.
Conclusion:
Thus, three methods to solve a system of linear equations are substitution method, elimination method and graphical method.
Want to see more full solutions like this?
Chapter 5 Solutions
College Algebra
- What is a system of linear equations in the variables x, y, and z?arrow_forwardWrite a uniform motion problem similar to Example 4.15 that relates to where you live with your friends or family members. Then translate to a system of equations and solve it.arrow_forwardUse the system of three equations in three variables to solve each problem. Work schedules A college student earns 198.50 per week working three part-time jobs. Half of his 30-hour work week is spent cooking hamburgers at a fast-food chain, earning 5.70 per hour. In addition, the student earns 6.30 per hour doing janitorial work. How many hours per week does the student work at each jobarrow_forward
- College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningAlgebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningCollege Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillElementary AlgebraAlgebraISBN:9780998625713Author:Lynn Marecek, MaryAnne Anthony-SmithPublisher:OpenStax - Rice University