To solve the system of equations using elimination, follow these steps:
Given equations:
1) \( 3x - y = 28 \)
2) \( 3x + y = 14 \)
First, add the two equations together to eliminate \( y \):
\[ (3x - y) + (3x + y) = 28 + 14 \]
This simplifies to:
\[ 3x - y + 3x + y = 42 \]
\[ 6x = 42 \]
\[ x = 7 \]
Now that you have \( x = 7 \), substitute this value back into either of the original equations to find \( y \). Let's use the second equation:
\[ 3x + y = 14 \]
\[ 3(7) + y = 14 \]
\[ 21 + y = 14 \]
\[ y = 14 - 21 \]
\[ y = -7 \]
So the solution to the system is \( (7, -7) \).
Therefore, the correct answer is:
\[ (7, -7) \]
10.
Solve the system using elimination.
3x – y = 28
3x + y = 14
(–4, 8)
(–7, 7)
(8, –4)
(7, –7)
1 answer