Question

≠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?

Answer 1

Answer:

C. 3x+6y=9  and-2x-4y=4

Step-by-step explanation:

Given

Steps:

• Multiply equation 1 by 2

• Multiply equation 2 by 3

• Add the results together

The attachment completes the question

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

Multiply by 2: $-2x+4y=4 ===> -4x + 8y = 4$

Multiply by 3: $-3x+6y=6 ===> -6x + 12y = 12$

Add together

$-4x - 6x + 8y + 12y = 4 + 12$

$-10x + 20y = 16$

B. 3x+y=12  and -3x+6y=6

Multiply by 2: $3x+y=12 ===> 6x + 2y = 24$

Multiply by 3: $-3x+6y=6 ==> -9x + 18y = 18$

Add together:

$6x - 9x + 2y + 18y = 24 + 18$

$-3y + 10y = 42$

C. 3x+6y=9  and-2x-4y=4

Multiply by 2: $3x+6y=9 ===>6x + 12y = 18$

Multiply by 3: $-2x-4y=4 ===> -6x - 12y = 12$

Add together:

$6x - 6x + 12y - 12y = 18 + 12$

$0 = 30$

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