The question asks you to solve the given system of equations using the elimination method:

1. $2x + 3y = 8$
2. $x - y = 9$

Step 1: Make the coefficients of one variable equal

To eliminate $x$, we multiply the second equation by $2$, so the system becomes:

$2x + 3y = 8$ $2x - 2y = 18$

Step 2: Subtract the equations

Subtract the second equation from the first:

$(2x + 3y) - (2x - 2y) = 8 - 18$

Simplify:

$5y = -10$

Solve for $y$:

$y = -2$

Step 3: Substitute $y = -2$ into one of the original equations

Substitute $y = -2$ into $x - y = 9$:

$x - (-2) = 9$

$x + 2 = 9$

$x = 7$

Final Answer:

The solution is $(x, y) = (7, -2)$.

Correct option: $(7, -2)$.

Would you like further details or have any questions?

5 Related Questions:

1. How do you use substitution to solve a system of equations?
2. What is the difference between elimination and substitution methods?
3. How do you verify a solution to a system of equations?
4. Can a system of equations have no solution or infinite solutions? Why?
5. How is elimination useful for solving equations with fractions?

Tip:

Always double-check your work by substituting your solution back into both original equations!