# Ron-Jon comes home from school, opens the door to his home and calls out: “Mom! Are you home? I want…

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### Tanong

Ron-Jon comes home from school, opens the door to his home and calls out: "Mom! Are you home? I want to show you something!" He is proud because he has solved the system

[tex]begin{cases} mathsf{3x:+:3y:=:9} \ mathsf{2x:+:y:=:4} end{cases}[/tex]

and wants to show his mother how he did it. Lena-Jon, Ron-Jon's sister, sits in the living room when he comes in. She says: "Maybe I should have a look first before you show mom?" He shows her his solution and it looks like this.

Step 1:

[tex]2x : + : y : = : 4 \ y : = : 4 : - : 2x[/tex]

Step 2:

[tex]3x + y(4 - 2x) = 9 \ 3x + 12 - 6x = 9 \ - 3x = - 3 \ x = 1[/tex]

Step 3:

[tex]2x + y = 4 \ 2x + 1 = 4 \ 2x = 3 \ x = 1.5[/tex]

Lena-Jon finds a mistake in Ron-Jon's solution and helps him correct it. Describe the mistake Ron-Jon and state the correct solution.

### Mga sagot sa #1 sa Tanong: Ron-Jon comes home from school, opens the door to his home and calls out: "Mom! Are you home? I want to show you something!" He is proud because he has solved the system

[tex]begin{cases} mathsf{3x:+:3y:=:9} \ mathsf{2x:+:y:=:4} end{cases}[/tex]

and wants to show his mother how he did it. Lena-Jon, Ron-Jon's sister, sits in the living room when he comes in. She says: "Maybe I should have a look first before you show mom?" He shows her his solution and it looks like this.

Step 1:

[tex]2x : + : y : = : 4 \ y : = : 4 : - : 2x[/tex]

Step 2:

[tex]3x + y(4 - 2x) = 9 \ 3x + 12 - 6x = 9 \ - 3x = - 3 \ x = 1[/tex]

Step 3:

[tex]2x + y = 4 \ 2x + 1 = 4 \ 2x = 3 \ x = 1.5[/tex]

Lena-Jon finds a mistake in Ron-Jon's solution and helps him correct it. Describe the mistake Ron-Jon and state the correct solution.

In step 1, y was isolated correctly. In step 2, the expression from step 1 was substituted into the second equation and x was solved for correctly. In step 3, y was substituted with the value of x. This is the mistake.

- (
**See****the****picture**)

To solve it correctly, we should substitute the x with 1 and calculate the value of y.

- 2x + y = 4

x = **1**

- 2 ·
**1**

Multiply

- 2 + y = 4

LRS - 2 = RHS - 2

- y = 2

╰┈➤ The value of y is **2**.

**#****S****t****u****d****y****T****i****m****e**

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