Question

Find the solution to the system of equations, x + 3y = 7 and 2x + 4y = 8.

1. Isolate x in the first equation: x = 7 − 3y
2. Substitute the value for x into the second equation: 2(7 − 3y) + 4y = 8
3. Solve for y: 14 − 6y + 4y = 8
14 − 2y = 8
−2y = −6
y = 3
4. Substitute y into either original equation: x = 7 − 3(3)
5. Write the solution as an ordered pair: (
,
)
 

Answer 1

Let's go through the solution step by step based on the equations you've provided:

1. Start with the first equation:
\[ x + 3y = 7 \]
Isolate \( x \):
\[ x = 7 - 3y \]

2. Substitute \( x = 7 - 3y \) into the second equation:
\[ 2x + 4y = 8 \]
\[ 2(7 - 3y) + 4y = 8 \]
\[ 14 - 6y + 4y = 8 \]

3. Simplify and solve for \( y \):
\[ 14 - 2y = 8 \]
\[ -2y = 8 - 14 \]
\[ -2y = -6 \]
\[ y = 3 \]

4. Substitute \( y = 3 \) back into the equation \( x = 7 - 3y \):
\[ x = 7 - 3(3) \]
\[ x = 7 - 9 \]
\[ x = -2 \]

5. Finally, write the solution as an ordered pair:
\[ (-2, 3) \]

So, the solution to the system of equations is \( (-2, 3) \).