Q. 35 Solve each system of equations. ... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 11: Q. 35 (page 714)

Solve each system of equations. If the system has no solution, say that it is inconsistent.
$\{\begin{matrix} \frac{1}{2} x + \frac{1}{3} y = 3 \\ \frac{1}{4} x - \frac{2}{3} y = - 1 \end{matrix}$

Short Answer

Expert verified

The solution of the given system of equation is $x = 4, y = 3; (4, 3)$ .

Step by step solution

Step 1. Given information.

The given equations are:

$\begin{array}{rcl} \frac{1}{2} x + \frac{1}{3} y & = & 3 \\ \frac{1}{4} x - \frac{2}{3} y & = & - 1 \end{array}$

Step 2. Determine one variable in terms of another variable.

The first equation can be written as:

$\begin{array}{rcl} \frac{1}{2} x + \frac{1}{3} y & = & 3 \\ \frac{1}{2} x & = & 3 - \frac{1}{3} y \\ \frac{1}{2} x & = & \frac{9 - y}{3} \\ x & = & \frac{2 (9 - y)}{3} \end{array}$

Step 3. Determine the value of one variable.

Substitute the above value in the second equation.

$\begin{array}{rcl} \frac{1}{4} (\frac{2 (9 - y)}{3}) - \frac{2}{3} y & = & - 1 \\ \frac{9 - y}{6} - \frac{2}{3} y & = & - 1 \\ \frac{9 - y - 4 y}{6} & = & - 1 \\ 9 - 5 y & = & - 6 \end{array}$

On further simplification, we get

$\begin{array}{rcl} - 5 y & = & - 6 - 9 \\ - 5 y & = & - 15 \\ y & = & \frac{- 15}{- 5} \\ y & = & 3 \end{array}$

Step 4. Determine the value of another variable.

Substitute $y = 3$ in $x = \frac{2 (9 - y)}{3}$ .

$\begin{array}{rcl} x & = & \frac{2 (9 - 3)}{3} \\ x & = & \frac{2 (6)}{3} \\ x & = & 2 (2) \\ x & = & 4 \end{array}$

The solution of the given system of equation is $x = 4, y = 3; (4, 3)$ .

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91影视

Solve each system of equations. If the system has no solution, say that it is inconsistent.
$\{\begin{matrix} \frac{1}{2} x + \frac{1}{3} y = 3 \\ \frac{1}{4} x - \frac{2}{3} y = - 1 \end{matrix}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Determine one variable in terms of another variable.

Step 3. Determine the value of one variable.

Step 4. Determine the value of another variable.

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91影视

Solve each system of equations. If the system has no solution, say that it is inconsistent.12x+13y=314x-23y=-1

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Determine one variable in terms of another variable.

Step 3. Determine the value of one variable.

Step 4. Determine the value of another variable.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Calculus

Probability and Statistics

Statistics

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Study anywhere. Anytime. Across all devices.

Solve each system of equations. If the system has no solution, say that it is inconsistent.
$\{\begin{matrix} \frac{1}{2} x + \frac{1}{3} y = 3 \\ \frac{1}{4} x - \frac{2}{3} y = - 1 \end{matrix}$