Q. 189 Solve a System of Linear Equatio... [FREE SOLUTION]

91影视

Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 4: Q. 189 (page 432)

Solve a System of Linear Equations with Three Variables:
$\{\begin{cases} x - 2 y + 3 z = 1 \\ x + y - 3 z = 7 \\ 3 x - 4 y + 5 z = 7 \end{cases}$

Short Answer

Expert verified

Solution of the system of equations is $(5 + z, 2 + 2 z, z)$ .

Step by step solution

Step 1. Given Information.

We have been given system of equations :

$\{\begin{cases} x - 2 y + 3 z = 1 \\ x + y - 3 z = 7 \\ 3 x - 4 y + 5 z = 7 \end{cases}$

Step 2. Using Elimination method to solve system of equations.

Multiply $- 1$ in second equation to get opposite coefficients of $x$

$x + y - 3 z = 7$

$- x - y + 3 z = - 7$

Step 3. Add the equations to get two variable equation.

Add the equations : $\{\begin{cases} x - 2 y + 3 z = 1 \\ - x - y + 3 z = - 7 \end{cases}$

$- 3 y + 6 z = - 6$

$- y + 2 z = - 2$

Step 4. Multiply -3 in first equation, to get opposite coefficients of x.

$x - 2 y + 3 z = 1$

$- 3 (x - 2 y + 3 z) = - 3 (1)$

$- 3 x + 6 y - 9 z = - 3$

Now, add the equations : $\{\begin{cases} - 3 x + 6 y - 9 z = - 3 \\ 3 x - 4 y + 5 z = 7 \end{cases}$

$2 y - 4 z = 4$

$y - 2 z = 2$

Step 5. Add the equations.

$\{\begin{cases} - y + 2 z = - 2 \\ y - 2 z = 2 \end{cases}$

$0 = 0$

This is True.

System has infinitely many solutions.

Step 6. Represent the solution showing how x,y are dependent on z.

So, we have $y - 2 z = 2$

$y = 2 z + 2$

And, equation $x - 2 y + 3 z = 1$

Substitute -

$x - 2 (2 z + 2) + 3 z = 1$

$x - 4 z - 4 + 3 z = 1$

$x - z = 5$

$x = 5 + z$

Solution of the system of equations is $(5 + z, 2 + 2 z, z)$ .

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91影视

Solve a System of Linear Equations with Three Variables:
$\{\begin{cases} x - 2 y + 3 z = 1 \\ x + y - 3 z = 7 \\ 3 x - 4 y + 5 z = 7 \end{cases}$

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Using Elimination method to solve system of equations.

Step 3. Add the equations to get two variable equation.

Step 4. Multiply -3 in first equation, to get opposite coefficients of x.

Step 5. Add the equations.

Step 6. Represent the solution showing how x,y are dependent on z.

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91影视

Solve a System of Linear Equations with Three Variables:x-2y+3z=1x+y-3z=73x-4y+5z=7

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Using Elimination method to solve system of equations.

Step 3. Add the equations to get two variable equation.

Step 4. Multiply -3 in first equation, to get opposite coefficients of x.

Step 5. Add the equations.

Step 6. Represent the solution showing how x,y are dependent on z.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Probability and Statistics

Applied Mathematics

Pure Maths

Calculus

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Solve a System of Linear Equations with Three Variables:
$\{\begin{cases} x - 2 y + 3 z = 1 \\ x + y - 3 z = 7 \\ 3 x - 4 y + 5 z = 7 \end{cases}$