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Lesson Example Discussion Quiz: Class Homework

Step-1

Title: System of Linear Equations with no Solutions

Grade: 1400-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 \$4x + 5y = 5\$, \$2x + ky = 9\$, then find the value of k?
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	Hint	First, we will compare 4x + 5y = 5 with equation(1) and 2x + ky = 9 with equation (2). So by comparing the coefficients, It can be written as	\$a_1 = 4, a_2 = 2\$, \$b_1 = 5, b_2 = k\$, \$c_1 = 5, c_2 = 9\$
5	Step	Now substitute the values in equation (3) then simplify	\$ 4/2 = 5/k ne 5/9 \$ \$ 4/2 = 5/k \$ \$ 4k = 10 \$
6	Step	The value of k is	\$ (\cancel(4^1)k)/\cancel4^1 = \cancel10^5/\cancel4^2 \$ \$ k = 5/2 \$
7	Step	Therefore, the value of k is \$ 5/2\$.
8	Choice.A	Choice A is incorrect. It represents the inverse of the correct value of k	\$ k = 2/5\$
9	Choice.B	Choice B is incorrect. It represents a negative value, but the value of k is positive	\$ k = -5/2\$
10	Choice.C	Choice C is incorrect. It represents the inverse of the correct value of k and is negative	\$ k = -2/5\$
11	Choice.D	Choice D is correct. It represents the correct value that we got by using the formula	\$ k = 5/2\$
12	Answer	Option	D
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
\$4x + 5y = 5\$, \$2x + ky = 9\$, then find the value of k?

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)

Hint

First, we will compare 4x + 5y = 5 with equation(1)
and 2x + ky = 9 with equation (2).
So by comparing the coefficients, It can be written as

\$a_1 = 4, a_2 = 2\$,
\$b_1 = 5, b_2 = k\$,
\$c_1 = 5, c_2 = 9\$

Step

Now substitute the values in equation (3) then simplify

\$ 4/2 = 5/k ne 5/9 \$

\$ 4/2 = 5/k \$

\$ 4k = 10 \$

Step

The value of k is

\$ (\cancel(4^1)k)/\cancel4^1 = \cancel10^5/\cancel4^2 \$
\$ k = 5/2 \$

Step

Therefore, the value of k is \$ 5/2\$.

Choice.A

Choice A is incorrect. It represents the inverse of the correct value of k

\$ k = 2/5\$

Choice.B

Choice B is incorrect. It represents a negative value, but the value of k is positive

\$ k = -5/2\$

Choice.C

Choice C is incorrect. It represents the inverse of the correct value of k and is negative

\$ k = -2/5\$

Choice.D

Choice D is correct. It represents the correct value that we got by using the formula

\$ k = 5/2\$

Answer

Option

Sumup

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