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ExtremeBDS [4]
3 years ago
12

Solve the system of equations by the substitution method.

Mathematics
2 answers:
kati45 [8]3 years ago
6 0

Answer:

Option A

The solution set is (-8,2)


Step-by-step explanation:

Given is a system of equations as

x+2y=-4\\3x+5y=-14\\

We have to solve this by substitution method

Consider the first equation and write x in terms of y

[tex]x=-2y-4[/tex]

Substitute in II equation as follows:

3(-2y-4)+5y=-14\\-6y-12+5y=-14\\-y=12-14=-2\\y=2\\x=-4-2(2)\\=-8

The system has a unique solution and the solution set is

(-8,2)

larisa86 [58]3 years ago
5 0

Answer:

Choice A is correct answer.

(-8,2)

Step-by-step explanation:

We have given two equations.

x+2y = -4                        eq(1)

3x+5y = -14                    eq(2)

We have to find the values of x and y by subtitution method.

Adding -2y to both sides of eq(1), we have

x+2y-2y = -4-2y

x = -4-2y                 eq(3)

Subtitute above value of x in eq(2), we have

3(-4-2y)+5y = -14

-12-6y +5y = -14

Adding like terms, we have

-12 -y = -14

Adding 12 to both sides of above equation , we have

12-12-y  = 12-14

-y = -2

Cancelling negative sign of both sides, we have

y = 2

Putting the value of y in eq(3) , we have

x = -4-2(2)

x = -4-4

x = -8

hence, the solution set (-8,2).

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Hey!

------------------------------------------------

First Equation:

2x + 3 = -7

2x + 3 - 3 = -7 - 3 (Subtract 7 to both sides)

2x = -10

2x/2 = -10/2 (Divide 2 to both sides)

x = -5

------------------------------------------------

Second Equation:

4.5x - 7 = 20

4.5x + (-7) + 7 = 20 + 7 (Add 7 to both sides)

4.5x = 27

4.5x/4.5 = 27/4.5 (Divide 4.5 to both sides)

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------------------------------------------------

Third Equation:

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-3x + 7 - 7 = 28 - 7 (Subtract 7 to both sides)

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x = -7

------------------------------------------------

Answers:

2x + 3 = -7 → x = -5

4.5x - 7 = 20 → x = 6

-3x + 7 = 28 → x = -7

------------------------------------------------

Hope This Helped! Good Luck!

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