To solve this system of equations using substitution, let's proceed step-by-step.

The given equations are: $x + y = 10$ $-x - 2y = -14$

Step 1: Solve for $x$ in terms of $y$ using the first equation

From the first equation: $x = 10 - y$

Step 2: Substitute $x = 10 - y$ into the second equation

Substitute this expression for $x$ into the second equation: $-(10 - y) - 2y = -14$ Now, expand and simplify: $-10 + y - 2y = -14$ $-10 - y = -14$

Step 3: Solve for $y$

Add 10 to both sides: $-y = -4$ Multiply by $-1$: $y = 4$

Step 4: Substitute $y = 4$ back into $x = 10 - y$

Substitute $y = 4$ into $x = 10 - y$: $x = 10 - 4 = 6$

Solution

The solution to the system is: $(x, y) = (6, 4)$

Would you like further details or have any questions?

Here are some additional questions to expand your understanding:

1. How would the solution change if the equations had different constants?
2. Can substitution be used if both equations are in standard form?
3. How would you verify the solution for a system of equations?
4. What are alternative methods to solve systems of equations besides substitution?
5. How does the substitution method work for systems with no solution or infinite solutions?

Tip: Always check your solution by substituting both values back into the original equations.