Greetings!
Answer:
Option 4
Explanation:
Firstly, we need to make the two x's or the two y numbers the same. Lets multiply the second equation by 2:
(2x + 3y = 5 ) * 2 =
4x + 6y = 10
Now, subtract the second equation from the first one:
(4x - y = -11) - (4x + 6y = 10)
4x - 4x = 0
-y - 6y = -7y
-11 - 10 = -21
-7y = -21
Divide both sides by -7:
y = 3
Plug 3 into the first equation as y:
4x - 3 = -11
4x = -11 + 3
4x = -8
x = -2
So x = -2 and y = 3. We need to find one of the options that equals this.
Option 1)
-4x - 9y = -21
-10y = -30
40x - 90y = -210
-90y = -270
40x - 0 = 40x
-90y - - 90y = -90 + 90 = 0y
-210 - -270 = -210 + 270 = 60
40x = 60
x = 1.5
We already know this isn't equivalent because the x value is not the x value of the given equation.
Option 2)
4x + 3y = 5
2y = -6
_______
8x + 6y = 10
6y = -18
8x - 0 = 8x
6y - 6y = 0
10 - -18 = 10 + 18 = 28
8x = 28
x = 3.5
So we know this isn't equivalent because again, the x value isn't the same as the given equation.
Option 3
7x - 3y = -11
9x = -6
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63x - 27y = -99
63x = -42
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63x - 63x = 0
-27y - 0 = -27y
-99 - - 42 = -99 + 42 = -57
-27y = -57
-9y = -19
9y = 19
y = 19/9
So we know this one isn't equivalent as the y value isn't the same as the given equation.
Option 4
12x - 3y = -33
14x = -28
x = -28/14 = -2
12(-2) - 3y = -33
-24 - 3y = -33
-3y = -33 + 24
-3y = -9
y = 9/3
y = 3
So x = -2 and y = -3 which is the same as the first equation.
Hope this helps!