mandilynn22
contestada

Solve the system of equations by the substitution method.

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

A.
The solution set is { ? }
​(Type an ordered​ pair.)
B.
There are infinitely many solutions. The solution set is {(x,y) | ? }
​(Type an​ equation.)
C.
There is no solution. The solution set is empty set.

Respuesta :

Answer:

Option A

The solution set is (-8,2)


Step-by-step explanation:

Given is a system of equations as

[tex]x+2y=-4\\3x+5y=-14\\[/tex]

We have to solve this by substitution method

Consider the first equation and write x in terms of y

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

Substitute in II equation as follows:

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

The system has a unique solution and the solution set is

(-8,2)

zainebamir540

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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