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Examine the system of equations. Which is an equivalent form of the first equation that when added to the second equation eliminates the y terms?

-5/8x + 3/4y = 12
8x + 12y = 11

A. 10x - 12y = -192
B. - 10x + 12y = 192
C. 5x - 12y = 96
D. - 5x + 12y = 96

Respuesta :

texaschic101
if u multiply the first equation by -16, u get : 10x - 12y = - 192

and when added to the other equation, it will eliminate the y terms.

Answer:

Option B - [tex]-10x+12y=192[/tex]

Step-by-step explanation:

Given : The system of equations

[tex]-\frac{5}{8}x+\frac{3}{4}y=12[/tex]

[tex]8x+12y=11[/tex]

To find : Which is an equivalent form of the first equation that when added to the second equation eliminates the y terms?

Solution :

To get an equivalent equation we solve the equation by taking least common denominator,

[tex]-\frac{5}{8}x+\frac{3}{4}y=12[/tex]

[tex]\frac{-5x+6y}{8}=12[/tex]

[tex]-5x+6y=12\times 8[/tex]

[tex]-5x+6y=96[/tex]

Multiply equation by 2,

[tex]-10x+12y=192[/tex]

Therefore, option B is correct.

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