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Lesson Example Discussion Quiz: Class Homework

Step-5

Title: System of Linear Equations with Infinite Solutions

Grade: 1400-a Lesson: S1-L7

Explanation: Hello Students, time to practice and review the steps for the problem.

Lesson Steps

Step	Type	Explanation	Answer
1	Problem	Show that the following system of equations has an infinite solution: - 14x + 21y = 35 and 2x - 3y = - 5.
2	Step	Given system of the equations are	-14x + 21y = 35 Equation(1) 2x - 3y = - 5 Equation(2)
3	Formula:	The linear system is	\$ a_1x + b_1y = c_1 \$ \$ a_2x + b_2y = c_2 \$
4	Hint	By comparing with the linear system, we get	\$ a_1 = - 14, b_1 = 21 ,c_1 = 35 , a_2 = 2 , b_2 = - 3,c_2 = - 5 \$
5	Step	Now, the ratios are:	\$ (a_1/a_2) = (\cancel(-14)^7 )/(\cancel(2)^1 ) = - 7 \$ \$ (b_1/b_2) = (\cancel(21)^7 )/(\cancel(- 3)^1 ) = - 7 \$ \$ (c_1/c_2) = (\cancel(35)^7 )/(\cancel(- 5)^1 ) = - 7 \$ \$ (a_1/a_2) = (b_1/b_2) = (c_1/c_2) \$
6	Step	Therefore, the given system of equations has infinitely many solutions.
7	Choice.A	This option indicates that the ratios of coefficients are not equal, which is not true in this case	\$-7 ne 7 ne - 7 \$
8	Choice.B	This option indicates that the ratios of coefficients are not equal, which is not true in this case	\$ -1/7 ne - 7 = - 7\$
9	Choice.C	This option indicates that the ratios of coefficients are equal, but this is not true	5 = 5 = 5
10	Choice.D	This option indicates that all the ratios of coefficients are equal, which is true in this case. So, this option is correct	-7 = - 7 = - 7
11	Answer	Option	D
12	Sumup	Can you briefly tell me what you’ve learned and understood in today’s lesson?

Step

Type

Explanation

Answer

Problem

Show that the following system of equations has an infinite solution:
- 14x + 21y = 35 and 2x - 3y = - 5.

Step

Given system of the equations are

-14x + 21y = 35 Equation(1)

2x - 3y = - 5 Equation(2)

Formula:

The linear system is

\$ a_1x + b_1y = c_1 \$

\$ a_2x + b_2y = c_2 \$

Hint

By comparing with the linear system, we get

\$ a_1 = - 14, b_1 = 21 ,c_1 = 35 , a_2 = 2 , b_2 = - 3,c_2 = - 5 \$

Step

Now, the ratios are:

\$ (a_1/a_2) = (\cancel(-14)^7 )/(\cancel(2)^1 ) = - 7 \$
\$ (b_1/b_2) = (\cancel(21)^7 )/(\cancel(- 3)^1 ) = - 7 \$
\$ (c_1/c_2) = (\cancel(35)^7 )/(\cancel(- 5)^1 ) = - 7 \$
\$ (a_1/a_2) = (b_1/b_2) = (c_1/c_2) \$

Step

Therefore, the given system of equations has infinitely many solutions.

Choice.A

This option indicates that the ratios of coefficients are not equal, which is not true in this case

\$-7 ne 7 ne - 7 \$

Choice.B

This option indicates that the ratios of coefficients are not equal, which is not true in this case

\$ -1/7 ne - 7 = - 7\$

Choice.C

This option indicates that the ratios of coefficients are equal, but this is not true

5 = 5 = 5

Choice.D

This option indicates that all the ratios of coefficients are equal, which is true in this case. So, this option is correct

-7 = - 7 = - 7

Answer

Option

Sumup

Can you briefly tell me what you’ve learned and understood in today’s lesson?