≠A student took a system of equations, multiplied the first equation by and the second equation by , then added the results together. Based on this, she concluded that there were no solutions. Which system of equations could she have started with?

Question

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Respuesta :

MrRoyal MrRoyal · Answer 1 · 2021-02-20T02:46:45+01:00

Answer:

C. 3x+6y=9 and-2x-4y=4

Step-by-step explanation:

Given

Steps:

The attachment completes the question

(a): -2x+4y=4 and -3x+6y=6

Multiply by 2: [tex]-2x+4y=4 ===> -4x + 8y = 4[/tex]

Multiply by 3: [tex]-3x+6y=6 ===> -6x + 12y = 12[/tex]

Add together

[tex]-4x - 6x + 8y + 12y = 4 + 12[/tex]

[tex]-10x + 20y = 16[/tex]

B. 3x+y=12 and -3x+6y=6

Multiply by 2: [tex]3x+y=12 ===> 6x + 2y = 24[/tex]

Multiply by 3: [tex]-3x+6y=6 ==> -9x + 18y = 18[/tex]

Add together:

[tex]6x - 9x + 2y + 18y = 24 + 18[/tex]

[tex]-3y + 10y = 42[/tex]

C. 3x+6y=9 and-2x-4y=4

Multiply by 2: [tex]3x+6y=9 ===>6x + 12y = 18[/tex]

Multiply by 3: [tex]-2x-4y=4 ===> -6x - 12y = 12[/tex]

Add together:

[tex]6x - 6x + 12y - 12y = 18 + 12[/tex]

[tex]0 = 30[/tex]

This is the equation the student could have used because 0 = 30 means the equation has no solution.