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Lesson Example Discussion Quiz: Class Homework

Step-4

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	Find the value of l and m: 32l = - 8m + 11 and 48l + 12m = 17
2	Step	Given equations are	\$32l = - 8m + 11\$ \$48l + 12m = 17\$
3	Step	Now rewrite the first equation	\$32l + 8m = 11\$ …….equation (1) \$48l + 12m = 17\$ …….equation (2)
4	Step	The value of l is	\$l = - \cancel8^1/\cancel32^4 m + 11/32\$ \$l = - 1/4 m + 11/32\$
5	Clue	Substitute the value of 'l' in equation (2)	\$ 48(- 1/4 m + 11/32) + 12m = 17\$ \$- \cancel(48^(12))/\cancel4^1 y + 11/\cancel(32)^2 \times \cancel(48)^3 + 12m = 17\$ \$ - 12m + 33/2 + 12m = 17\$
6	Step	Move the constants to the right side and then simplify	\$ - 12y + 12y = 17 - 33/2 \$ \$ 0 = (34 - 33)/2 \$ \$ 0 = 1/2 \$
7	Step	We get \$0 = 1/2\$. This cannot be true.
8	Choice.A	Choice A is incorrect. There cannot be infinitely solutions since there are no solutions	Finite solutions
9	Choice.B	Choice B is correct. It reflects the outcome of the solution process, indicating that the system of equations does not have a solution	No solutions
10	Choice.C	Choice C is incorrect. This implies that the system has a specific, finite number of solutions	Infinite solutions
11	Choice.D	Choice D is incorrect. It does not accurately reflect the outcome of the solution process	None of these
12	Answer	Option	B
13	Sumup	Can you summarize what you’ve understood in the above steps?

Step

Type

Explanation

Answer

Problem

Find the value of l and m:
32l = - 8m + 11 and 48l + 12m = 17

Step

Given equations are

\$32l = - 8m + 11\$
\$48l + 12m = 17\$

Step

Now rewrite the first equation

\$32l + 8m = 11\$ …….equation (1)
\$48l + 12m = 17\$ …….equation (2)

Step

The value of l is

\$l = - \cancel8^1/\cancel32^4 m + 11/32\$

\$l = - 1/4 m + 11/32\$

Clue

Substitute the value of 'l' in equation (2)

\$ 48(- 1/4 m + 11/32) + 12m = 17\$

\$- \cancel(48^(12))/\cancel4^1 y + 11/\cancel(32)^2 \times \cancel(48)^3 + 12m = 17\$

\$ - 12m + 33/2 + 12m = 17\$

Step

Move the constants to the right side and then simplify

\$ - 12y + 12y = 17 - 33/2 \$

\$ 0 = (34 - 33)/2 \$

\$ 0 = 1/2 \$

Step

We get \$0 = 1/2\$. This cannot be true.

Choice.A

Choice A is incorrect. There cannot be infinitely solutions since there are no solutions

Finite solutions

Choice.B

Choice B is correct. It reflects the outcome of the solution process, indicating that the system of equations does not have a solution

No solutions

Choice.C

Choice C is incorrect. This implies that the system has a specific, finite number of solutions

Infinite solutions

Choice.D

Choice D is incorrect. It does not accurately reflect the outcome of the solution process

None of these

Answer

Option

Sumup

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