Solve the following system of equations using elimination:

[tex]\[ 2x - 3y = 6 \][/tex]
[tex]\[ 2x - 3y = 8 \][/tex]

A. (0, 4)
B. (4, 0)
C. (0, 3)
D. (3, 0)
E. Infinite Solutions
F. No Solution



Answer :

To solve the given system of equations using the elimination method, follow these steps:

1. Write down the system of equations:

[tex]\[ \begin{cases} 2x - 3y = 6 \\ 2x - 3y = 8 \end{cases} \][/tex]

2. Compare the two equations:

[tex]\[ 2x - 3y = 6 \quad \text{(Equation 1)} \][/tex]
[tex]\[ 2x - 3y = 8 \quad \text{(Equation 2)} \][/tex]

3. Subtract Equation 2 from Equation 1 to eliminate [tex]\(x\)[/tex] and [tex]\(y\)[/tex]:

[tex]\[ (2x - 3y) - (2x - 3y) = 6 - 8 \][/tex]
Simplifying this, we get:
[tex]\[ 0 = -2 \][/tex]

4. Interpret the result:

The equation [tex]\(0 = -2\)[/tex] is a contradiction, meaning that it's not possible for the same [tex]\(x\)[/tex] and [tex]\(y\)[/tex] values to satisfy both equations simultaneously. This tells us that there is no solution to the system of equations.

Therefore, the solution to the system of equations [tex]\(2x - 3y = 6\)[/tex] and [tex]\(2x - 3y = 8\)[/tex] is:

[tex]\[ \boxed{\text{No Solution}} \][/tex]