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SIZIF [17.4K]
3 years ago
8

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

Mathematics
2 answers:
Allisa [31]3 years ago
6 0
4x − y = −11
<span>2x + 3y = 5
lets multiply the second equation by -2 and add it to the first:
</span><span> 4x − y = −11
</span>-4x - 6y = -10
------------------
0  - 7y = -21
y = -21/-7
y = 3
now we substitute this result in the first equation to find x:
<span>4x − y = −11
</span>4x - 3 = -11
4x = -8
x = -8/4
x = 2
so the solution is y = 3 and x =2


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



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


7x − 3y = −11
<span>9x = −6
</span>we solve for x:
<span>9x = −6
</span>x = -6/9
x = -2/3
then we substitute in the first equation the result found:
<span>7x − 3y = −11
</span><span>7(-2/3) − 3y = −11
</span>-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 <span>y = 19/9


</span>12x − 3y = −33
<span>14x = −28
</span>we solve for x:
<span>14x = −28
</span>x = -28/14
x = -2
then we substitute in the first equation:
<span>12x − 3y = −33
</span><span>12(-2) − 3y = −33
</span>-24 - 3y = -33
3y = 9
y = 3
then the solution is x = -2 and y = 3
Pavlova-9 [17]3 years ago
6 0

4x-y=-11

2x+3y=5

Solve 4x-y=-11 for y

Add -4x to both sides

4x-y+-4x=-11+-4x

-y=-4x-11

Divide both sides by -1

-y/-1=-4x-11/-1

y=4x+11

Substitute 4x+11 for y in 2x +3y=5

2x+3y=5

2x+3(4x+11)=5

Simplify both sides of the equation

14x+33=5

Add -33 to both sides

14x+33+-33=5+-33

14x=-28

Divide both sides by 14

14x/14=-28/14

x=-2

Substitute -2 for x in y= 4x+11

y=4x+11

y=(4)(-2)+11

Simplify both sides of the equation

y=3


Let's see if D will equal the same

14x=-28

12x-3y=-33

Solve 14x =-28 for x

14x/14=-28/14

x=-2

Substitute -2 for x in 12x-3y=-33

12x-3y=-33

(12)(-2)-3y=-33

Simplify both sides of the equation

-3y-24=-33

Add 24 to both sides

-3y-24+24=-33+24

-3y=-9

Divide both sides by -3

-3y/-3=-9/-3

y=3

Answer D

x=-2 and y=3


Sorry for taking so long with it but I hope you understand , have a great night

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