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]
