Question

Suppose you are given the system of equations x = y - 4 8x + 7y = 14
.
a. Which variable would you replace in the substitution​ process?
b. What expression would replace that​ variable?

Answer 1

Solve the system using elimination.


3x + 16y = 6

3x - 16y = 6

(Type an ordered​ pair.)

Answer 2

Solve the system using elimination.


7x + 4y = 30

4x - 4y = -8

​(Simplify your answer. Type an ordered​ pair.)

Answer 3

a. In the substitution process, we would replace the variable x.

b. The expression that would replace the variable x is (y - 4).

Answer 4

By subtracting the second equation from the first equation, we can eliminate the x terms:

(3x + 16y) - (3x - 16y) = 6 - 6
16y + 16y = 0
32y = 0
y = 0

Now we can substitute the value of y into either of the original equations. Let's use the first equation:

3x + 16(0) = 6
3x = 6
x = 2

Therefore, the solution to the system of equations is the ordered pair (x, y) = (2, 0).

Answer 5

To solve the system using elimination, we can add the two equations together to eliminate the y terms:

(7x + 4y) + (4x - 4y) = 30 + (-8)
7x + 4x + 4y - 4y = 22
11x = 22
x = 2

Now we can substitute the value of x into either of the original equations. Let's use the first equation:

7(2) + 4y = 30
14 + 4y = 30
4y = 30 - 14
4y = 16
y = 4

Therefore, the solution to the system of equations is the ordered pair (x, y) = (2, 4).