Question

4.

Solve the given system, using the substitution method.


y = 4x – 6

8x – 2y = 14



A.

(14, 12)


B.

(12, 14)


C.

There are an infinite number of solutions.


D.

There is no solution.


3.


Solve the given system, using the substitution method.


y = 3x – 7

6x – 2y = 12


A.

There is no solution.


B.

(12, 14)


C.

(14, 12)


D.

There are an infinite number of solutions.


5.


Solve, using the substitution method.


y + 2x = 7

14 – 4x = 2y


A.

The solution is (1, 5)


B.

The solution is (21, 0)


C.

There are an infinite number of solutions.


D.

There is no solution.

Answer 1

4. No solution

Explanation:

To solve a system of equations, find the (x,y) solution that satisfies both equations. One method that can be used is substitution. It is done by substituting one function into the other function and simplify.

Substitute y = 4x - 6 into 8x - 2y = 14.

8x - 2(4x - 6) = 14

8x - 8x + 12 = 14

12 = 14 FALSE

Since the variable was eliminated and a false statement was found, there is no solution to this system.

Solve 3 and 5 similarly. If the variable is eliminated again, but a true statement is fund then the solution is infinite. If the variable is not eliminated then substitute it back into one equation to find the other.