To solve the system of equations using substitution, follow these steps:

Step 1: Solve one equation for one variable

From the first equation, $2x - y = 7$, solve for $y$ in terms of $x$:

$y = 2x - 7$

Step 2: Substitute into the second equation

Now substitute $y = 2x - 7$ into the second equation $-6x + 3y = 21$:

$-6x + 3(2x - 7) = 21$

Step 3: Simplify and solve for $x$

Distribute the $3$ on the left-hand side:

$-6x + 6x - 21 = 21$

Simplifying the equation:

$0x - 21 = 21$

This simplifies to:

$-21 = 21$

Step 4: Conclusion

Since this is a contradiction (an impossible statement), there is no solution to this system of equations. The system is inconsistent.

Would you like more details on why this system is inconsistent or have other questions?

Related Questions:

1. How do you solve a system of equations using elimination?
2. What does it mean for a system of equations to have no solution?
3. Can you explain systems of equations that have infinitely many solutions?
4. What are the different methods for solving a system of linear equations?
5. How can you check if a system of equations is consistent before solving?

Tip:

When solving systems of equations, always check for contradictions or identities early on to identify special cases like no solutions or infinitely many solutions.