Chapter 11: Q. 24 (page 714)

Solve each system of equations. If the system has no solution, say that it is inconsistent.
$\{\begin{cases} 2 x + 4 y = \frac{2}{3} \\ 3 x - 5 y = - 1 \end{cases}$

Short Answer

Expert verified

The solution of the given system of equation is $x = - \frac{5}{3}, y = 1; (- \frac{5}{3}, 1)$ .

Step by step solution

Step 1. Given information.

The given equations are:

$\begin{array}{rcl} 2 x + 4 y & = & \frac{2}{3} \\ 3 x - 5 y & = & - 10 \end{array}$

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

The second equation can be written as:

$\begin{array}{rcl} 3 x - 5 y & = & - 10 \\ 3 x & = & - 10 + 5 y \\ x & = & \frac{5 y - 10}{3} \end{array}$

Step 3. Determine the value of one variable.

Substitute the above value in the first equation.

$\begin{array}{rcl} 2 (\frac{5 y - 10}{3}) + 4 y & = & \frac{2}{3} \\ \frac{10 y - 20}{3} + 4 y & = & \frac{2}{3} \\ \frac{10 y - 20 + 12 y}{3} & = & \frac{2}{3} \\ 22 y - 20 & = & 2 \\ 22 y & = & 2 + 20 \\ y & = & \frac{22}{22} \\ y & = & 1 \end{array}$

Step 4. Determine the value of another variable.

Substitute $y = 1$ in $x = \frac{5 y - 10}{3}$ .

$\begin{array}{rcl} x & = & \frac{5 (1) - 10}{3} \\ x & = & \frac{5 - 10}{3} \\ x & = & - \frac{5}{3} \end{array}$

The solution of the given system of equation is $x = - \frac{5}{3}, y = 1; (- \frac{5}{3}, 1)$ .

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Solve each system of equations. If the system has no solution, say that it is inconsistent.
$\{\begin{cases} 2 x + 4 y = \frac{2}{3} \\ 3 x - 5 y = - 1 \end{cases}$

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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Solve each system of equations. If the system has no solution, say that it is inconsistent.2x+4y=233x-5y=-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

Statistics

Calculus

Decision Maths

Theoretical and Mathematical Physics

Logic and Functions

Pure Maths

Study anywhere. Anytime. Across all devices.

Solve each system of equations. If the system has no solution, say that it is inconsistent.
$\{\begin{cases} 2 x + 4 y = \frac{2}{3} \\ 3 x - 5 y = - 1 \end{cases}$