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Lesson Example Discussion Quiz: Class Homework

Step-2

Title: System of Linear Equations with no Solutions

Grade: 1300-a Lesson: S1-L8

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

Lesson Steps

Step	Type	Explanation	Answer
1	Problem	If there is no solution to the linear equation system 3a - b = 2, ma + 4b = 8, then find the value of m?
2	Step	Consider the two linear equations are	\$ a_1x + b_1x = c_1 \$ …….eq (1) \$ a_2x + b_2x = c_2 \$ …….eq (2)
3	Formula:	If equation (1) and equation (2) have no solution then we can write,	\$ a_1/a_2 = b_1/b_2 ne c_1/c_2 \$ …….equation (3)
4	Hint	First, we will compare 3a - b = 2 with equation (1) and ma + 4b = 8 with equation (2). So by comparing the coefficients, we can write	\$a_1 = 3,a_2 = m\$, \$b_1 = - 1,b_2 = 4\$, \$c_1 = 2,c_2 = 8\$
5	Clue	Now substitute the values in equation (3)	\$ 3/m = - 1/4 ne 2/8 \$ …….equation (3)
6	Step	Now taking the first two parts of the above equation, we get	\$ 3/m = - 1/4 \$
7	Step	After cross-multiplication and simplification, we get	12 = - m - 12 = - (- m) m = - 12
8	Step	Therefore, the value of m is - 12.
9	Choice.A	Choice A is incorrect. This value would not make the coefficients of a and b proportional in the same manner as required for no solution	\$m = 1/12\$
10	Choice.B	Choice B is incorrect. After inspecting the coefficients, we found that the value of 'm' does not meet the required condition	\$m = -1/12\$
11	Choice.C	Choice C is correct. After analyzing the coefficients, we verified that the value of m is appropriate, maintaining the validity of the equality	m = - 12
12	Choice.D	Choice D is incorrect. Upon examining the coefficients, we found that the value of m does not meet the required condition	m = 12
13	Answer	Option	C
14	Sumup	Can you summarize what you’ve understood in the above steps?

Step

Type

Explanation

Answer

Problem

If there is no solution to the linear equation system
3a - b = 2, ma + 4b = 8, then find the value of m?

Step

Consider the two linear equations are

\$ a_1x + b_1x = c_1 \$ …….eq (1)
\$ a_2x + b_2x = c_2 \$ …….eq (2)

Formula:

If equation (1) and equation (2) have no solution then we can write,

\$ a_1/a_2 = b_1/b_2 ne c_1/c_2 \$ …….equation (3)

Hint

First, we will compare 3a - b = 2 with equation (1)
and ma + 4b = 8 with equation (2).
So by comparing the coefficients, we can write

\$a_1 = 3,a_2 = m\$,
\$b_1 = - 1,b_2 = 4\$,
\$c_1 = 2,c_2 = 8\$

Clue

Now substitute the values in equation (3)

\$ 3/m = - 1/4 ne 2/8 \$ …….equation (3)

Step

Now taking the first two parts of the above equation, we get

\$ 3/m = - 1/4 \$

Step

After cross-multiplication and simplification, we get

12 = - m
- 12 = - (- m)
m = - 12

Step

Therefore, the value of m is - 12.

Choice.A

Choice A is incorrect. This value would not make the coefficients of a and b proportional in the same manner as required for no solution

\$m = 1/12\$

Choice.B

Choice B is incorrect. After inspecting the coefficients, we found that the value of 'm' does not meet the required condition

\$m = -1/12\$

Choice.C

Choice C is correct. After analyzing the coefficients, we verified that the value of m is appropriate, maintaining the validity of the equality

m = - 12

Choice.D

Choice D is incorrect. Upon examining the coefficients, we found that the value of m does not meet the required condition

m = 12

Answer

Option

Sumup

Can you summarize what you’ve understood in the above steps?