Question

Fill in the blank(s) to correctly complete each sentence. To solve the system $$\begin{aligned}&3 x+y=4\\&7 x+8 y=-2\end{aligned}$$ by substitution, it is easiest to begin by solving equation (1) for the variable _____ and then substituting into equation ( 2 ), because no fractions will appear in the algebraic work.

Name: Problem 4, Chapter 5: Student's Solutions Manual for College Algebra
Uploaded: 2021-05-16T08:07:17-08:00
Duration: 1 min 7 s
Channel: Tanishq Gupta
Description: Fill in the blank(s) to correctly complete each sentence. To solve the system 3 x+y=4 7 x+8 y=-2 by substitution, it is easiest to begin by solving equation (1) for the variable and then substituting into equation ( 2 ), because no fractions will appear in the algebraic work.

   Fill in the blank(s) to correctly complete each sentence.
To solve the system
$$\begin{aligned}&3 x+y=4\\&7 x+8 y=-2\end{aligned}$$
by substitution, it is easiest to begin by solving equation (1) for the variable _____ and then substituting into equation ( 2 ), because no fractions will appear in the algebraic work.

Student's Solutions Manual for College Algebra

Margaret L. Lial,… 12th Edition

Chapter 5, Problem 4

Instant Answer

Solved by Expert Tanishq Gupta

05/16/2021

Step 1

This is done by subtracting $3x$ from both sides of the equation. This gives us: $$y = 4 - 3x$$ Show more…

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Fill in the blank(s) to correctly complete each sentence. To solve the system $$\begin{aligned}&3 x+y=4\\&7 x+8 y=-2\end{aligned}$$ by substitution, it is easiest to begin by solving equation (1) for the variable _____ and then substituting into equation ( 2 ), because no fractions will appear in the algebraic work.

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Key Concepts

System of Linear Equations

A system of linear equations consists of two or more linear equations involving the same set of variables. The goal is to find values for these variables that satisfy all the equations simultaneously, and such systems are fundamental in algebra and many applied fields.

Substitution Method

The substitution method involves solving one of the equations for one variable in terms of the others and then substituting this expression into the remaining equations. This method reduces the system to a simpler form, making it easier to isolate and solve for the unknown variables.

Variable Isolation Strategy

Choosing which variable to isolate can impact the simplicity of the subsequent algebra. It is advantageous to isolate a variable that leads to expressions without fractions or unnecessary complexity, thereby streamlining the calculation process and minimizing errors.

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