To solve the system of equations:
[tex]\[ y = x + 3 \][/tex]
[tex]\[ 2x + y = 9 \][/tex]
we can follow these steps:
1. Substitute the first equation into the second equation:
Since [tex]\( y = x + 3 \)[/tex], we can substitute [tex]\( x + 3 \)[/tex] for [tex]\( y \)[/tex] in the second equation.
[tex]\[ 2x + (x + 3) = 9 \][/tex]
2. Simplify and solve for [tex]\( x \)[/tex]:
Combine the [tex]\( x \)[/tex]-terms:
[tex]\[ 2x + x + 3 = 9 \][/tex]
[tex]\[ 3x + 3 = 9 \][/tex]
Subtract 3 from both sides:
[tex]\[ 3x = 6 \][/tex]
Divide by 3:
[tex]\[ x = 2 \][/tex]
3. Substitute [tex]\( x \)[/tex] back into the first equation to find [tex]\( y \)[/tex]:
Using [tex]\( x = 2 \)[/tex] in [tex]\( y = x + 3 \)[/tex]:
[tex]\[ y = 2 + 3 \][/tex]
[tex]\[ y = 5 \][/tex]
Thus, the solution to the system of equations is [tex]\( (x, y) = (2, 5) \)[/tex].
4. Verify the solution with multiple choice options:
We are given the options:
- [tex]\( (2, 5) \)[/tex]
- [tex]\( (5, 2) \)[/tex]
- [tex]\( (-2, 5) \)[/tex]
- [tex]\( (2, -5) \)[/tex]
5. Identifying the correct option:
The solution [tex]\( (2, 5) \)[/tex] matches the first option [tex]\( O(2, 5) \)[/tex].
Therefore, the correct solution to the system of equations is [tex]\( (2, 5) \)[/tex], corresponding to option 1.
