Chapter 3: Q6. (page 142)

Solve each system of equations.
$\begin{matrix} r - 3 s + t = 4 \\ 3 r - 6 s + 9 t = 5 \\ 4 r - 9 s + 10 t = 9 \end{matrix}$

Short Answer

Expert verified

The solution has infinitely many solutions.

Step by step solution

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

Given system of equations are

$\begin{matrix} r - 3 s + t = 4 \\ 3 r - 6 s + 9 t = 5 \\ 4 r - 9 s + 10 t = 9 \end{matrix}$

Multiplying first equation by and subtracting with the second equation, we get

$\begin{matrix} - 12 s + 9 s + 4 t - 10 t = 16 - 9 \\ - 3 s - 6 t = 7 \end{matrix}$

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

System of equations with two variables are

$\begin{array}{l} - 3 s - 6 t = 7 \\ - 3 s - 6 t = 7 \end{array}$

Therefore, the equation $- 3 s - 6 t = 7$ has infinitely many solutions.

Step-3 –Evaluating the value of r

Since, s andt has infinitely many values and sor has many values.

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Solve each system of equations.
$\begin{matrix} r - 3 s + t = 4 \\ 3 r - 6 s + 9 t = 5 \\ 4 r - 9 s + 10 t = 9 \end{matrix}$

Short Answer

Step by step solution

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

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

Step-3 –Evaluating the value of r

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Solve each system of equations.r-3s+t=43r-6s+9t=54r-9s+10t=9

Short Answer

Step by step solution

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

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

Step-3 –Evaluating the value of r

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Calculus

Mechanics Maths

Theoretical and Mathematical Physics

Logic and Functions

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Solve each system of equations.
$\begin{matrix} r - 3 s + t = 4 \\ 3 r - 6 s + 9 t = 5 \\ 4 r - 9 s + 10 t = 9 \end{matrix}$