Question

Solve the following system of equations with the substitution method. Write your answers as an Ordered Pair. If infinitely many solutions exist, enter
(oo). If no solution exists, enter DNE
x + 20y= 50
-12x + y = - 118

Answer 1

To solve the given system of equations using the substitution method, we can follow these steps:

1. Start with the two equations:
\[
1) \quad x + 20y = 50
\]
\[
2) \quad -12x + y = -118
\]

2. First, we can solve the first equation for \( x \):
\[
x = 50 - 20y
\]

3. Now we can substitute this expression for \( x \) into the second equation:
\[
-12(50 - 20y) + y = -118
\]

4. Simplifying this equation:
\[
-600 + 240y + y = -118
\]
\[
241y - 600 = -118
\]

5. Add 600 to both sides:
\[
241y = 482
\]

6. Now divide by 241 to find \( y \):
\[
y = \frac{482}{241} = 2
\]

7. Now that we have \( y \), substitute back to find \( x \):
\[
x = 50 - 20(2)
\]
\[
x = 50 - 40 = 10
\]

Thus, the solution to the system of equations is:
\[
(x, y) = (10, 2)
\]

The final answer as an ordered pair is:
\[
\boxed{(10, 2)}
\]