2x-y=7  -6x+3y=21 solve with substitution

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.

2x - y = 7  -6x + 3y = 21 solve with substitution

Solve the system of equations 2x - y = 7 and -6x + 3y = 21 using the substitution method. This step-by-step guide covers key algebraic concepts, explains how to identify an inconsistent system, and is suitable for students in Grades 9-10.

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