Question

Which of these strategies would eliminate a variable in the system of equations? \begin{cases} 2x - 5y = 13 \\\\ -3x + 2y = 13 \end{cases} ⎩ ⎪ ⎪ ⎨ ⎪ ⎪ ⎧ ​ 2x−5y=13 −3x+2y=13 ​

Answer 1

Answer and Step-by-step explanation:

Given the system of equations:

2x – 5y = 13

–3x + 2y = 13

We can decide to eliminate either x or y in order to solve the simultaneous equations.

1. To eliminate x:

Multiply the first equation by the coefficient of x in the second equation and multiply the second equation by the coefficient of x in the first equation. By doing this the coefficients of x in the equations would be the same and subtracting them to be equal to zero becomes easy, thus eliminating that variable.

The coefficient of x in the second equation is –3, if we multiply the first equation by it we have:

–6x+15y = –39

The coefficient of x in the first equation is 2, if we multiply the second equation by it we have:

–6x+4y = 26

Subtracting the resulting equations we have:

11y = –65 and x is eliminated.

2. To eliminate y:

Multiply the first equation by the coefficient of y in the second equation and multiply the second equation by the coefficient of y in the first equation. By doing this the coefficients of y in the equations would be the same and subtracting them to be equal to zero becomes easy, thus eliminating that variable.

The coefficient of y in the second equation is 2, if we multiply the first equation by it we have:

4x–10y = 26

The coefficient of y in the first equation is –5, if we multiply the second equation by it we have:

15x–10y = –65

Subtracting the resulting equations we have:

–11x = 91 and y is eliminated.