# Solving system of linear equations: soln's for 2/5x + 1/3(2y+1)=1/5

#### Illvoices

##### Junior Member
2/5x + 1/3(2y+1)=1/5
Consider the system of equations above. Which of the following statements is true?

• (Choice A)A

There is only one solution [FONT=KaTeX_Main](x,y)([FONT=KaTeX_Math]x,[FONT=KaTeX_Math]y)left parenthesis, x, comma, y, right parenthesis and [FONT=KaTeX_Main]x + y[FONT=KaTeX_Math]x+[FONT=KaTeX_Math]yx, plus, y
is positive.

• [/FONT]
[/FONT]

• (Choice B)B

There is only one solution [FONT=KaTeX_Main](x,y)([FONT=KaTeX_Math]x,[FONT=KaTeX_Math]y)left parenthesis, x, comma, y, right parenthesis and [FONT=KaTeX_Main]x + y[FONT=KaTeX_Math]x+[FONT=KaTeX_Math]yx, plus, y
is negative.

[/FONT]

[/FONT]
[/FONT]
[/FONT][/FONT]
[/FONT]

• (Choice C)C

There are infinitely many solutions.

• (Choice D)D

There are no solutions.

[/FONT]
[/FONT]
[/FONT]How do I solve for this equation and why'd they show that multiplying by 15 in both equation was a correct choice in the explanation?[/FONT]

#### Dr.Peterson

##### Elite Member
2/5x + 1/3(2y+1)=1/5
Consider the system of equations above. Which of the following statements is true?

• (Choice A)A

There is only one solution [FONT=KaTeX_Main](x,y)([FONT=KaTeX_Math]x,[FONT=KaTeX_Math]y)left parenthesis, x, comma, y, right parenthesis and [FONT=KaTeX_Main]x + y[FONT=KaTeX_Math]x+[FONT=KaTeX_Math]yx, plus, y
is positive.

• [/FONT]
[/FONT]

• (Choice B)B

There is only one solution [FONT=KaTeX_Main](x,y)([FONT=KaTeX_Math]x,[FONT=KaTeX_Math]y)left parenthesis, x, comma, y, right parenthesis and [FONT=KaTeX_Main]x + y[FONT=KaTeX_Math]x+[FONT=KaTeX_Math]yx, plus, y
is negative.
[/FONT][/FONT][/FONT]
[/FONT][/FONT]
[/FONT]

• (Choice C)C

There are infinitely many solutions.

• (Choice D)D

There are no solutions.

[/FONT]
[/FONT][/FONT]How do I solve for this equation and why'd they show that multiplying by 15 in both equation was a correct choice in the explanation?[/FONT]
I only see one equation, not a system!

You seem to have copied and pasted from some source that repeats every expression in three forms. Please type it in yourself, or else edit carefully, so that others can read it without struggling to understand.

In addition, I can't tell you why they said what they did without seeing what they said. From the one equation you show, certainly multiplying by the LCD, 15, is one appropriate step, but it is not absolutely necessary. Are you thinking it is an invalid thing to do, or just that something else could be done?

#### sinx

##### Junior Member
2/5x + 1/3(2y+1)=1/5

How do I solve for this equation and why'd they show that multiplying by 15 in both equation was a correct choice in the explanation?
they multiply by 15 to get both the 3 and 5 out of the denominator(s).
[or you can multiply by 5 and 3 one step at a time.]