Question

Solve the system by substitution. x – 3y = 4 2x – 6y = 8 A. no solution B. x = 4, y = 0 C. x = 0, y = 0 D. infinite solutions

Answer 1

A

Explanation:

1. Isolate the x-term in the first equation:

x-3y=4 -> x=3y+4

2. Substitute 3y+4 in for x in the second equation and solve

2(3y+4)-6y=8 : Distribute the 2

6y+8-6y=8 : Combine like terms

8=8

3. Isolate the y-term in the first equation:

x-3y=4 -> -3y=-x+4

a. Solve for y:

(-3y=-x+4)/-3 : Divide by -3

y=(1/3)x-(4/3)

4. Substitute (1/3)x-(4/3) in for y in the second equation and solve:

2x-6((1/3)x-(4/3))=8 : Distribute the -6

2x-2x+8=8 : Combine like terms

8=8

Explanation:

When you solve a system of equations and get a true statement-

The lines are parallel.

Parallel lines will never intersect, so there is no solution.

Answer 2

The correct answer is option D.

Explanation:

if the pair of equation has one or more than one solution then it is said to be consistent.

• Only one solution , then independent system.
• More than one solution , then dependent system.

if the pair of equation has no solution then it is said to be inconsistent.

Given : x - 3y = 4 ...[1]

2x - 6y = 8 ...[2]

Solution :

Solving equations with the help of Substituting methods:

x - 3y = 4

x = 4 +3y

Putting value of x from [1] in [2]:

`2(4+3y)-6y=8`

`8+6y-6y=8`

`6y=6y`

0 = 0

Given , system of equation will have infinite solution. Hence consistent and dependent.

The given system of equations will have infinite solutions.