solving a linear system using algebra: the method of substitution.     x=1-y and x=1-2y

To solve the given linear system using the **substitution method**, follow these steps:

The system of equations is:

\[
x = 1 - y
\]
\[
x = 1 - 2y
\]

### Step 1: Set the equations equal to each other.

Since both equations equal \( x \), you can set the right-hand sides equal to each other:

\[
1 - y = 1 - 2y
\]

### Step 2: Solve for \( y \).

Simplify the equation to isolate \( y \):

\[
1 - y = 1 - 2y
\]
Subtract 1 from both sides:
\[
-y = -2y
\]
Add \( 2y \) to both sides:
\[
y = 0
\]

### Step 3: Substitute \( y = 0 \) into one of the original equations.

Now substitute \( y = 0 \) into either of the original equations. Let's use the first one:

\[
x = 1 - y
\]

Substitute \( y = 0 \):

\[
x = 1 - 0 = 1
\]

### Final solution:

The solution to the system is:
\[
x = 1, \quad y = 0
\]

### Solution as an ordered pair:
\[
(x, y) = (1, 0)
\]

Would you like more details on this method or have any questions?

### Relative questions:
1. How does the substitution method compare to the elimination method?
2. Can the substitution method be used for non-linear systems of equations?
3. What if both equations had no solution—how would substitution show this?
4. How can we check if the solution to the system is correct?
5. How do substitution and graphing methods relate for solving systems of equations?

### Tip:
Always double-check your solution by substituting the values back into the original equations to ensure they satisfy both.

solving a linear system using algebra: the method of substitution. x=1-y and x=1-2y

Learn how to solve the linear system of equations x = 1 - y and x = 1 - 2y using the substitution method. This step-by-step solution walks through setting equations equal, solving for variables, and finding the solution as an ordered pair. Ideal for students in Grades 8-10.

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