Westonci.ca is the best place to get answers to your questions, provided by a community of experienced and knowledgeable experts. Explore in-depth answers to your questions from a knowledgeable community of experts across different fields. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.
Sagot :
To solve the system of equations:
1. [tex]\( 3x = 27 \)[/tex]
2. [tex]\( x + y = 7 \)[/tex]
Let's follow these steps:
### Step 1: Solve for [tex]\( x \)[/tex] in the first equation
The first equation is:
[tex]\[ 3x = 27 \][/tex]
To solve for [tex]\( x \)[/tex], divide both sides by 3:
[tex]\[ x = \frac{27}{3} \][/tex]
So,
[tex]\[ x = 9 \][/tex]
### Step 2: Substitute the value of [tex]\( x \)[/tex] into the second equation
Now we substitute [tex]\( x = 9 \)[/tex] into the second equation:
[tex]\[ x + y = 7 \][/tex]
This becomes:
[tex]\[ 9 + y = 7 \][/tex]
### Step 3: Solve for [tex]\( y \)[/tex]
To find [tex]\( y \)[/tex], subtract 9 from both sides:
[tex]\[ y = 7 - 9 \][/tex]
So,
[tex]\[ y = -2 \][/tex]
### Step 4: Identify the solution
The solution to the system of equations is the ordered pair [tex]\((x, y)\)[/tex], which we've found to be:
[tex]\[ (9, -2) \][/tex]
### Step 5: Verify the obtained solution
Let's verify by substituting [tex]\( x = 9 \)[/tex] and [tex]\( y = -2 \)[/tex] back into the original equations to ensure they hold true:
For the first equation:
[tex]\[ 3x = 27 \][/tex]
[tex]\[ 3(9) = 27 \][/tex]
[tex]\[ 27 = 27 \][/tex] (True)
For the second equation:
[tex]\[ x + y = 7 \][/tex]
[tex]\[ 9 + (-2) = 7 \][/tex]
[tex]\[ 7 = 7 \][/tex] (True)
The solution satisfies both equations, confirming that the correct solution is indeed:
[tex]\[ \boxed{(9, -2)} \][/tex]
So, of the given options:
- [tex]\((-17, 24)\)[/tex]
- [tex]\((9, -2)\)[/tex]
- [tex]\((24, -17)\)[/tex]
- [tex]\((-2, 9)\)[/tex]
The correct solution to the system of equations is:
[tex]\[ \boxed{(9, -2)} \][/tex]
1. [tex]\( 3x = 27 \)[/tex]
2. [tex]\( x + y = 7 \)[/tex]
Let's follow these steps:
### Step 1: Solve for [tex]\( x \)[/tex] in the first equation
The first equation is:
[tex]\[ 3x = 27 \][/tex]
To solve for [tex]\( x \)[/tex], divide both sides by 3:
[tex]\[ x = \frac{27}{3} \][/tex]
So,
[tex]\[ x = 9 \][/tex]
### Step 2: Substitute the value of [tex]\( x \)[/tex] into the second equation
Now we substitute [tex]\( x = 9 \)[/tex] into the second equation:
[tex]\[ x + y = 7 \][/tex]
This becomes:
[tex]\[ 9 + y = 7 \][/tex]
### Step 3: Solve for [tex]\( y \)[/tex]
To find [tex]\( y \)[/tex], subtract 9 from both sides:
[tex]\[ y = 7 - 9 \][/tex]
So,
[tex]\[ y = -2 \][/tex]
### Step 4: Identify the solution
The solution to the system of equations is the ordered pair [tex]\((x, y)\)[/tex], which we've found to be:
[tex]\[ (9, -2) \][/tex]
### Step 5: Verify the obtained solution
Let's verify by substituting [tex]\( x = 9 \)[/tex] and [tex]\( y = -2 \)[/tex] back into the original equations to ensure they hold true:
For the first equation:
[tex]\[ 3x = 27 \][/tex]
[tex]\[ 3(9) = 27 \][/tex]
[tex]\[ 27 = 27 \][/tex] (True)
For the second equation:
[tex]\[ x + y = 7 \][/tex]
[tex]\[ 9 + (-2) = 7 \][/tex]
[tex]\[ 7 = 7 \][/tex] (True)
The solution satisfies both equations, confirming that the correct solution is indeed:
[tex]\[ \boxed{(9, -2)} \][/tex]
So, of the given options:
- [tex]\((-17, 24)\)[/tex]
- [tex]\((9, -2)\)[/tex]
- [tex]\((24, -17)\)[/tex]
- [tex]\((-2, 9)\)[/tex]
The correct solution to the system of equations is:
[tex]\[ \boxed{(9, -2)} \][/tex]
We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.