Explanation Given information: The system of equations x = − 3 y + 4 and 5 x + 4 y = − 2 and the substitution method. Formula Used: To solve a system of equations in two variables using the substitution method: 1. Pick any equation and rewrite it explicitly in terms of any one variable. 2. Now substitute this value of the variable in the other equation and solve for the variable present in the equation. 3. Now put the value of the solved variable in the explicit solution and obtain the other variable as well. 4. Now substitute the values back into the original equations to check the solution. Calculation: Consider the provided system: x = − 3 y + 4 5 x + 4 y = − 2 Note that the equation x = − 3 y + 4 is already written explicitly in terms of x . Thus, this system can be easily solved using the substitution method. Substitute, x = − 3 y + 4 in 5 x + 4 y = − 2 to obtain: 5 ( − 3 y + 4 ) + 4 y = − 2 − 15 y + 20 + 4 y = − 2 − 11 y = − 22 y = 2 Now substitute the value of y in x = − 3 y + 4 and solve for x

5th Edition

ISBN: 9781259616754

Author: Julie Miller, Molly O'Neill, Nancy Hyde

Publisher: McGraw-Hill Education

See similar textbooks

Videos

Question

Chapter 4.3, Problem 9PRE

To determine

To calculate: The solution of the system of equations x=−3y+4 and 5x+4y=−2 and determine why substitution method should be used to obtain the solution to the system.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 4.3, Problem 8PRE

Chapter 4.3, Problem 10PRE

Students have asked these similar questions

Solve for the matrix X: X (2 7³) x + ( 2 ) - (112) 6 14 8

5. Solve for the matrix X. (Hint: we can solve AX -1 = B whenever A is invertible) 2 3 0 Χ 2 = 3 1

Write p(x) = 6+11x+6x² as a linear combination of ƒ (x) = 2+x+4x² and g(x) = 1−x+3x² and h(x)=3+2x+5x²

Chapter 4 Solutions

Beginning and Intermediate Algebra

Ch. 4.1 - Determine whether the ordered paired is a solution...Ch. 4.1 - Determine whether the ordered paired is a solution...Ch. 4.1 - Solve the system by the graphing method. y = − 3 x...Ch. 4.1 - Solve the system by the graphing method. y = 2 x −...Ch. 4.1 - Solve the system by the graphing. 5. Ch. 4.1 - Solve the system by the graphing. 6. Ch. 4.1 - a. A______ of linear equations consists of two or...Ch. 4.1 - For Exercises 2-10, determine if the given point...Ch. 4.1 - Prob. 3PE Ch. 4.1 - Prob. 4PE

Knowledge Booster

$Algebra$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

The solution of the system of equations x = − 3 y + 4 and 5 x + 4 y = − 2 and determine why substitution method should be used to obtain the solution to the system.

Solution Summary: The author explains the substitution method used to solve a system of equations in two variables.

Videos

To calculate: The solution of the system of equations x=−3y+4 and 5x+4y=−2 and determine why substitution method should be used to obtain the solution to the system.

Want to see the full answer?

Chapter 4 Solutions