Question

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 ?
​(Type an​ equation.)
C.
There is no solution. The solution set is empty set.

Answer 1

Choice A is correct answer.

(-8,2)

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).

Answer 2

Option A

The solution set is (-8,2)

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)