/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 4 Determine whether the given valu... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 11: Problem 4

Determine whether the given values of \(x, y,\) and z are a solution of the system of equations. $$\begin{array}{r}x=.3, y=.7 \\\4 x-1.2 y=.36 \\\3.1 x+2 y=4.7\end{array}$$

Short Answer

Expert verified
Answer: No, the given values for x and y do not satisfy the system of equations.

Step by step solution

01

Substitute the given values into the first equation

Replace x with 0.3 and y with 0.7 in the first equation: $$4x - 1.2y = 0.36$$ $$4(0.3) - 1.2(0.7)$$ Now we will calculate the result.
02

Calculate the result of the first equation

Perform the multiplication and subtraction in the equation: $$1.2 - 0.84 = 0.36$$ Since the equation is true, we will proceed with substituting the values into the second equation.
03

Substitute the given values into the second equation

Replace x with 0.3 and y with 0.7 in the second equation: $$3.1x + 2y = 4.7$$ $$3.1(0.3) + 2(0.7)$$ Now we will calculate the result.
04

Calculate the result of the second equation

Perform the multiplication and addition in the equation: $$0.93 + 1.4 = 2.33$$ Since the equation 3.1x + 2y = 4.7 resulted in 2.33 = 4.7, which is not true, we can conclude that the given values for x and y are not a solution for the system of equations.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Substitution Method
The substitution method is a technique used to solve systems of linear equations. Here, you replace one variable with an expression obtained from another equation that involves the second variable. This way, you simplify the system to a single equation with one unknown, making it more manageable to solve.
  • You first need to express one variable in terms of the other using one of the equations.
  • Then, substitute this expression into the other equation to find the value of one variable.
  • Finally, use the found value to determine the second variable using the initial expression you derived.
This method is particularly useful when one variable is easily isolated. It helps simplify solving a system of equations, as seen in our exercise where specific values were substituted in place of the variables.
Checking Solutions
When you're given potential solutions for a system of equations, verifying them is crucial. Checking involves substituting these values into each equation of the system to ensure they hold true.
Replace each variable in the equations with the given numerical values. Perform the arithmetic operations following the order of operations. If both sides of the equation equal for all equations in the system, the given values are indeed a solution.
In our exercise, substituting the values in both equations revealed:
  • The first equation was valid since both sides equaled.
  • The second equation was not, as the sides did not match.
This verifies that the proposed values do not solve the entire system correctly.
Linear Equations
Linear equations involve variables with exponents of one, forming straight lines when graphed. A system of linear equations consists of two or more equations working together, each with their own intercepts and slopes on a graph.
In the given exercise, the system contains two linear equations:
  • 4x - 1.2y = 0.36
  • 3.1x + 2y = 4.7
Each equation presents a linear relationship between the variables. By solving these equations simultaneously, we are looking for common values of the variables that satisfy both equations, representing their intersection point on a graph.
Understanding linear equations is fundamental in determining the solutions of many mathematical and real-world problems, as they describe relationships between quantities.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

When Neil Simon planned to open his play London Suite, his producer, Emanuel Azenberg, made the following cost and revenue estimates for opening on Broadway or off Broadway,*$$\begin{array}{|l|c|c|} \hline & \text { On Broadway } & \text { Off Broadway } \\\\\hline \text { Initial cost to open' } & \mathrm{S} 1,295,000 & \$ 440,000 \\\\\hline \text { Weekly costs }^{\dagger} & \$ 206,500 & \$ 82,000 \\\\\hline \text { Weekly revenue } & \$ 250,500 & \$ 109,000 \\\\\hline\end{array}$$ For a production on Broadway that runs \(x\) weeks, find a linear equation that gives the (a) total revenue \(R\) (b) total cost \(C\) (c) total profit \(P\). (d) Do parts (a)-(c) for an off-Broadway production. (e) After how many weeks will the on-Broadway profit equal the off-Broadway profit? What is the profit then? (f) When would it be better to open off Broadway rather than on Broadway?

Find the values of \(c\) and \(d\) for which both given points lie on the given straight line. $$c x+d y=-6 ; \quad(1,3) and (-2,12)$$

Exercises \(57-60\) deal with the break-even point, which is the point at which revenue equals cost. The cost \(C\) of making \(x\) hedge trimmers is given by \(C=45 x+6000 .\) Each hedge trimmer can be sold for \(\$ 60\) (a) Find an equation that expresses the revenue \(R\) from selling \(x\) hedge trimmers. (b) How many hedge trimmers must be sold for the company to break even?

Use the elimination method to solve the system. $$\begin{aligned}&\frac{2}{x}+\frac{3}{y}=8\\\&\frac{3}{x}-\frac{1}{y}=1\end{aligned}$$

Certain circus animals are fed the same three food mixes: \(R, S,\) and \(T .\) Lions receive 1.1 units of \(R, 2.4\) units of \(S,\) and 3.7 units of \(T\) each day. Horses receive 8.1 units of \(R, 2.9\) units of \(S,\) and 5.1 units of \(T\) each day. Bears receive 1.3 units of \(R, 1.3\) units of \(S,\) and 2.3 units of \(T\) each day. If 16,000 units of \(R, 28,000\) units of \(S,\) and 44,000 units of \(T\) are available each day, how many of each type of animal can be supported?
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Geometry

Read Explanation

Applied Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.