Chapter 4: Q 124 (page 406)

Write an application problem similar to Example $4.14$ . Then translate to a system of equations and solve it.

Short Answer

Expert verified

The two required numbers are $\frac{5}{2}$ and $- \frac{5}{2}$ .

Step by step solution

Step 1. Identify the required numbers.

Lets take an example:

Assume $x$ and $y$ are the two numbers.

The sum of the two numbers is $0$ .

So, $x + y = 0 . . . . . . (i)$

One number is five less than the other.

So, $y = x - 5 . . . . . . . (i i)$

Therefore, the system of equations is $x + y = 0 y = x - 5$ .

Step 2. Substitute the value of y in equation (i).

Substitute the value of $y$ in equation (i),

$x + x - 5 = 0 2 x = 5 x = \frac{5}{2}$

Substituting $x = \frac{5}{2}$ in equation (ii),

$y = \frac{5}{2} - 5 y = \frac{5 - 10}{2} y = - \frac{5}{2}$

Step 3. Check the answer by substituting the values of x,y in the equations.

Substitute in equation (i),

$x + y = 0 \frac{5}{2} + (- \frac{5}{2}) = 0 0 = 0$

This is true.

Again, substitute in equation (ii),

$y = x - 5 - \frac{5}{2} = \frac{5}{2} - 5 - \frac{5}{2} = \frac{5 - 10}{5} - \frac{5}{2} = - \frac{5}{2}$

This is also true.

The two required numbers are $\frac{5}{2}$ and $- \frac{5}{2}$ .

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Write an application problem similar to Example $4.14$ . Then translate to a system of equations and solve it.

Short Answer

Step by step solution

Step 1. Identify the required numbers.

Step 2. Substitute the value of y in equation (i).

Step 3. Check the answer by substituting the values of x,y in the equations.

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Write an application problem similar to Example 4.14. Then translate to a system of equations and solve it.

Short Answer

Step by step solution

Step 1. Identify the required numbers.

Step 2. Substitute the value of y in equation (i).

Step 3. Check the answer by substituting the values of x,y in the equations.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Discrete Mathematics

Statistics

Calculus

Logic and Functions

Pure Maths

Study anywhere. Anytime. Across all devices.

Write an application problem similar to Example $4.14$ . Then translate to a system of equations and solve it.