Chapter 3: Q7. (page 142)

Solve each system of equations.
$\begin{array}{l} 2 r + 3 s - 4 t = 20 \\ 4 r - s + 5 t = 13 \\ 3 r + 2 s + 4 t = 15 \end{array}$

Short Answer

Expert verified

The solution is $r = 5, s = - 2, t = - 1 .$

Step by step solution

Step-1 –Using elimination to obtain two equations with two variables

Given system of equations are

$\begin{matrix} 2 r + 3 s - 4 t = 20 \\ 4 r - s + 5 t = 13 \\ 3 r + 2 s + 4 t = 15 \end{matrix}$

Multiplying second equation by 3 and adding to the first equation, we get

$\begin{matrix} 2 r + 12 r - 4 t + 15 t = 20 + 39 \\ 14 r + 11 t = 59 \end{matrix}$

Again multiplying second equation by 2 and adding to the third equation, we get

$\begin{matrix} 8 r + 3 r + 10 t + 4 t = 26 + 15 \\ 11 r + 14 t = 41 \end{matrix}$

Step-2 –Solving the system of two equations with two variables

System of two equations with two variables are

$\begin{matrix} 14 r + 11 t = 59 \\ 11 r + 14 t = 41 \end{matrix}$

Multiplying the first equation by 11 and second by 14 and subtracting them we get

$\begin{matrix} 121 t - 196 t = 649 - 574 \\ - 75 t = 75 \\ t = - 1 \end{matrix}$

Putting the value of in equation we get

$\begin{matrix} 14 r - 11 = 59 \\ 14 r = 59 + 11 \\ 14 r = 70 \\ r = 5 \end{matrix}$

Step-3 –Finding the value of using the value o f r and t

Putting the value of r and t in the equation $4 r - s + 5 t = 13$ we get,

$\begin{matrix} 4 (5) - s + 5 (- 1) = 13 \\ 20 - s - 5 = 13 \\ - s = 13 - 15 \\ - s = - 2 \\ s = 2 \end{matrix}$

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Solve each system of equations.
$\begin{array}{l} 2 r + 3 s - 4 t = 20 \\ 4 r - s + 5 t = 13 \\ 3 r + 2 s + 4 t = 15 \end{array}$

Short Answer

Step by step solution

Step-1 –Using elimination to obtain two equations with two variables

Step-2 –Solving the system of two equations with two variables

Step-3 –Finding the value of using the value o f r and t

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Solve each system of equations.2r+3s-4t=204r-s+5t=133r+2s+4t=15

Short Answer

Step by step solution

Step-1 –Using elimination to obtain two equations with two variables

Step-2 –Solving the system of two equations with two variables

Step-3 –Finding the value of using the value o f r and t

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Applied Mathematics

Geometry

Logic and Functions

Statistics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Solve each system of equations.
$\begin{array}{l} 2 r + 3 s - 4 t = 20 \\ 4 r - s + 5 t = 13 \\ 3 r + 2 s + 4 t = 15 \end{array}$