Choose the equivalent system of linear equations that will produce the same solution as the one given below.

4x − y = −11
2x + 3y = 5

a: −4x − 9y = −21
−10y = −30

b: 4x + 3y = 5
2y = −6

c: 7x − 3y = −11
9x = −6

d: 12x − 3y = −33
14x = −28

4x − y = −11
2x + 3y = 5
lets multiply the second equation by -2 and add it to the first:
 4x − y = −11
-4x - 6y = -10

0  - 7y = -21
y = -21/-7
y = 3
now we substitute this result in the first equation to find x:
4x − y = −11
4x - 3 = -11
4x = -8
x = -8/4
x = 2
so the solution is y = 3 and x =2

4x − 9y = −21
−10y = −30
we solve for y
−10y = −30
y = -30/-10
y = 3
and substitute in the first equation:
4x − 9y = −21
4x − 9(3) = −21
4x - 27 = -21
4x = 6
x = 6/4 = 3/2
so the solution is x = 3/2 and y = 3

 4x + 3y = 5
2y = −6
we solve for y:
2y = −6
y = -6/2
y = -3
we do substitute in the first equation:
 4x + 3y = 5
 4x + 3(-3) = 5
4x - 9 = 5
4x = 14
x = 14/4
x = 7/2
so the solution is x = 7/2 and y = -3

7x − 3y = −11
9x = −6
we solve for x:
9x = −6
x = -6/9
x = -2/3
then we substitute in the first equation the result found:
7x − 3y = −11
7(-2/3) − 3y = −11
-14/3 - 3y = -11
we multiply by 3 to eliminate fractions:
-14 - 9y = -33
9y = 19
y = 19/9
so the solution is x = -2/3 and y = 19/9

12x − 3y = −33
14x = −28
we solve for x:
14x = −28
x = -28/14
x = -2
then we substitute in the first equation:
12x − 3y = −33
12(-2) − 3y = −33
-24 - 3y = -33
3y = 9
y = 3
then the solution is x = -2 and y = 3

2.) is the most sense

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