Question
Fill in the blanks to explain one way to solve this system of equations using elimination.
6x + 2y = 14
5x – 2y = 8
First, add the two equations to get 11x =
. Then substitute
for x in either equation to get y =
.
6x + 2y = 14
5x – 2y = 8
First, add the two equations to get 11x =
. Then substitute
for x in either equation to get y =
.
Answers
GPT-4o mini
To solve the system of equations using elimination, we start with the two given equations:
1) \( 6x + 2y = 14 \)
2) \( 5x - 2y = 8 \)
First, we can add the two equations to eliminate \( y \):
Adding equation 1 and equation 2:
\[
(6x + 2y) + (5x - 2y) = 14 + 8
\]
This simplifies to:
\[
11x = 22
\]
Now, we can solve for \( x \):
\[
x = \frac{22}{11} = 2
\]
Next, we substitute \( x = 2 \) into either of the original equations to find \( y \). Let's use the first equation:
\[
6(2) + 2y = 14
\]
This simplifies to:
\[
12 + 2y = 14
\]
Now, solve for \( y \):
\[
2y = 14 - 12
\]
\[
2y = 2
\]
\[
y = 1
\]
To summarize, we fill in the blanks:
First, add the two equations to get \( 11x = 22 \). Then substitute \( 2 \) for \( x \) in either equation to get \( y = 1 \).
1) \( 6x + 2y = 14 \)
2) \( 5x - 2y = 8 \)
First, we can add the two equations to eliminate \( y \):
Adding equation 1 and equation 2:
\[
(6x + 2y) + (5x - 2y) = 14 + 8
\]
This simplifies to:
\[
11x = 22
\]
Now, we can solve for \( x \):
\[
x = \frac{22}{11} = 2
\]
Next, we substitute \( x = 2 \) into either of the original equations to find \( y \). Let's use the first equation:
\[
6(2) + 2y = 14
\]
This simplifies to:
\[
12 + 2y = 14
\]
Now, solve for \( y \):
\[
2y = 14 - 12
\]
\[
2y = 2
\]
\[
y = 1
\]
To summarize, we fill in the blanks:
First, add the two equations to get \( 11x = 22 \). Then substitute \( 2 \) for \( x \) in either equation to get \( y = 1 \).