To solve this system of linear equations by substitution, let’s go through the steps.

The system provided is: $2x = 12$ $x - 5y = -29$

Step 1: Solve for $x$ in terms of numbers.

From the first equation: $2x = 12$ Divide both sides by 2 to isolate $x$: $x = 6$

Step 2: Substitute $x = 6$ into the second equation.

Now we substitute $x = 6$ into the second equation: $6 - 5y = -29$

Step 3: Solve for $y$.

Subtract 6 from both sides: $-5y = -29 - 6$ $-5y = -35$ Now, divide by -5: $y = 7$

Solution

The solution to the system is: $(x, y) = (6, 7)$

Would you like more details on any step, or have any other questions?

Here are five related questions to further your understanding:

1. How would you solve the system if it were given with different coefficients, for example, $3x = 15$ and $x - 7y = -21$?
2. What happens if the substitution method results in a contradiction, like $0 = 5$?
3. Can you solve this system by the elimination method instead of substitution?
4. How can you determine if a system of equations has no solution, one solution, or infinitely many solutions?
5. How would you graphically represent the solution to this system?

Tip: When using substitution, always isolate one variable first, making it easier to substitute and solve the system accurately.