To solve the system of linear equations:

1. $2x - y = -3$
2. $-5x + y = 9$

we can use either the substitution or elimination method. Let's use the elimination method since the coefficients of $y$ in both equations are opposites.

Step 1: Add the Two Equations

Add the two equations to eliminate $y$:

$(2x - y) + (-5x + y) = -3 + 9$

Simplify:

$2x - 5x = -3 + 9$

$-3x = 6$

Step 2: Solve for $x$

Divide by -3:

$x = \frac{6}{-3} = -2$

Step 3: Substitute $x$ Back to Find $y$

Now substitute $x = -2$ into the first equation:

$2x - y = -3$

$2(-2) - y = -3$

$-4 - y = -3$

Add 4 to both sides:

$-y = -3 + 4$

$-y = 1$

Multiply by -1:

$y = -1$

Solution

The solution to the system of equations is:

$x = -2, \quad y = -1$

Would you like more details on these steps, or do you have any questions?

Here are 5 related questions to consider:

1. How do you solve a system of equations using the substitution method?
2. What happens when the coefficients of both variables are the same in both equations?
3. How can you graphically interpret the solution of a system of linear equations?
4. What methods can be used to solve a system of three linear equations?
5. How does the determinant help in solving a system of linear equations using matrices?

Tip: The elimination method is efficient when the coefficients of one variable are already opposites or can easily be made opposites by multiplication.