Which of these strategies would eliminate a variable in the system of equations?2x−5y=13 −3x+2y=13
A. Multiply the top equation by 2, multiply the bottom equation by 3, then add the equations.
B. Subtract the bottom equation from the top equation
C. Multiply the top equation by 3, multiply the bottom equation by 2, then add the equations.

We conclude that when we multiply the top equation by 3, multiply the bottom equation by 2, then add the equations, it would eliminate the variable 'x'.

Thus, option (C) is true.

Step-by-step explanation:

Given the system of the equation

2x−5y=13

−3x+2y=13

3(2x−5y) = 3(13)

6x - 15y = 39

2(−3x+2y) = 2(13)

-6x + 4y = 26

Adding both equations

6x - 15y = 39

+

-6x + 4y = 26

0x - 11y = 65

-11y = 65               ∵ x variable eliminates

Divide both sides by -11

y = -65/11

Therefore, we conclude that when we multiply the top equation by 3, multiply the bottom equation by 2, then add the equations, it would eliminate the variable 'x'.

Thus, option (C) is true.

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1

600,000,000,000, or 6e14

step-by-step explanation: