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?
a. In the substitution process, we would replace the variable x.
b. The expression that would replace the variable x is (y - 4).
Solve the system using elimination.
3x + 16y = 6
3x - 16y = 6
(Type an ordered pair.)
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).
Solve the system using elimination.
7x + 4y = 30
4x - 4y = -8
(Simplify your answer. Type an ordered pair.)
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).