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Lesson Example Discussion Quiz: Class Homework

Step-3

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 Sg - 7h = 9, 3g + 5h =11, then find the value of S?
2	Step	Consider the two linear equations are	\$ a_1x + b_1x = c_1 \$ …….equation (1) \$ a_2x + b_2x = c_2 \$ …….equation (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	Step	First, we will compare Sg - 7h = 9 with equation (1) and 3f + 5h = 11 with eequation (2). So by comparing the coefficients, we can write	\$a_1 = S,a_2 = 3\$, \$b_1 = - 7,b_2 = 5\$, \$c_1 = 9,c_2 = 11\$
5	Step	Now substitute the values in equation (3), and then simplify	\$ S/3 = - 7/5 ne 9/11 \$ …….equation (3) \$ S/3 = - 7/5 \$ \$ 5S = - 21\$
6	Step	Divide both sides by 5. After simplification, we get	\$ (\cancel(5^1)S)/\cancel5^1 = - 21/5\$ \$ S = - 21/5 \$
7	Step	Therefore, the value of S is \$ - 21/5 \$.
8	Choice.A	Choice A is correct. It represents the correct value by using the formula.	\$S = -21/5\$
9	Choice.B	Choice B is incorrect. It is the reciprocal of the correct answer	\$S = 5/21\$
10	Choice.C	Choice C is incorrect. This is the negation of the correct answer	\$S = 21/5\$
11	Choice.D	Choice D is incorrect. This is the reciprocal of the negation of the correct answer	\$S = -5/21\$
12	Answer	Option	A
13	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
Sg - 7h = 9, 3g + 5h =11, then find the value of S?

Step

Consider the two linear equations are

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

Step

First, we will compare Sg - 7h = 9 with equation (1)
and 3f + 5h = 11 with eequation (2).
So by comparing the coefficients, we can write

\$a_1 = S,a_2 = 3\$,
\$b_1 = - 7,b_2 = 5\$,
\$c_1 = 9,c_2 = 11\$

Step

Now substitute the values in equation (3), and then simplify

\$ S/3 = - 7/5 ne 9/11 \$ …….equation (3)

\$ S/3 = - 7/5 \$

\$ 5S = - 21\$

Step

Divide both sides by 5. After simplification, we get

\$ (\cancel(5^1)S)/\cancel5^1 = - 21/5\$

\$ S = - 21/5 \$

Step

Therefore, the value of S is \$ - 21/5 \$.

Choice.A

Choice A is correct. It represents the correct value by using the formula.

\$S = -21/5\$

Choice.B

Choice B is incorrect. It is the reciprocal of the correct answer

\$S = 5/21\$

Choice.C

Choice C is incorrect. This is the negation of the correct answer

\$S = 21/5\$

Choice.D

Choice D is incorrect. This is the reciprocal of the negation of the correct answer

\$S = -5/21\$

Answer

Option

Sumup

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