Question

Part A From the following system of equations, create a new equation by substituting the value of y from the first equation into the second equation. ​From the new equation, evaluate the value of x.

y = -x - 4

3x + y = 8

Answer 1

Part B:


The solution to the original system of equations [is also, is not] a solution to the new equation. Solve the system of equations by SUBSTITUTION.

6y + 5x = 8

x + 3y = -7

Answer 2

Part B:
1) The solution to the original system of equations [is also, is not] a solution to the new equation.


2) Solve the system of equations by SUBSTITUTION.

6y + 5x = 8

x + 3y = -7

Answer 3

To substitute the value of y from the first equation into the second equation, replace y in the second equation with (-x - 4):

3x + (-x - 4) = 8

Simplifying the equation, combining like terms:

2x - 4 = 8

Adding 4 to both sides of the equation:

2x = 12

Dividing both sides by 2:

x = 6

Therefore, the value of x is 6.

Answer 4

To solve the system of equations by substitution, we'll solve one equation for one variable and substitute it into the other equation.

Let's solve the second equation for x:
x = -7 - 3y

Now, substitute this value of x into the first equation:
6y + 5(-7 - 3y) = 8

Simplifying the equation:
6y - 35 - 15y = 8
-9y - 35 = 8
-9y = 8 + 35
-9y = 43

Dividing both sides by -9:
y = -43/9

Now, substitute the value of y back into the second equation to find x:
x + 3(-43/9) = -7

Simplifying the equation:
x - 129/9 = -7
x - 129/9 = -63/9
x = -63/9 + 129/9
x = 66/9

Simplifying the fraction:
x = 22/3

Therefore, the solution to the original system of equations is x = 22/3 and y = -43/9.

Answer 5

1) The solution to the original system of equations is also a solution to the new equation.

In the original system:
6y + 5x = 8 ------ (Equation 1)
x + 3y = -7 ------ (Equation 2)

To solve the system of equations by substitution, we'll solve Equation 2 for x and substitute it into Equation 1.

From Equation 2, we can solve for x:
x = -7 - 3y

Now, substitute this value of x into Equation 1:
6y + 5(-7 - 3y) = 8

Simplifying the equation:
6y - 35 - 15y = 8
-9y - 35 = 8
-9y = 43

Dividing both sides by -9:
y = -43/9

Now, substitute the value of y back into Equation 2 to find x:
x + 3(-43/9) = -7

Simplifying the equation:
x - 129/9 = -7
x - 129/9 = -63/9
x = -63/9 + 129/9
x = 66/9

Simplifying the fraction:
x = 22/3

Therefore, the solution to the original system of equations is x = 22/3 and y = -43/9, and this solution also satisfies the new equation.