Answer :
Let's determine whether the point [tex]\((2, 3)\)[/tex] is a solution to both equations in the given system.
### First Equation: [tex]\(2x - 4y = -8\)[/tex]
Substitute [tex]\(x = 2\)[/tex] and [tex]\(y = 3\)[/tex]:
[tex]\[ 2(2) - 4(3) = -8 \][/tex]
Calculate each term:
[tex]\[ 4 - 12 = -8 \][/tex]
Simplify:
[tex]\[ -8 = -8 \][/tex]
This holds true, so [tex]\((2, 3)\)[/tex] is a solution for the first equation.
### Second Equation: [tex]\(-3x + 5y = 9\)[/tex]
Substitute [tex]\(x = 2\)[/tex] and [tex]\(y = 3\)[/tex]:
[tex]\[ -3(2) + 5(3) = 9 \][/tex]
Calculate each term:
[tex]\[ -6 + 15 = 9 \][/tex]
Simplify:
[tex]\[ 9 = 9 \][/tex]
This also holds true, so [tex]\((2, 3)\)[/tex] is a solution for the second equation.
### Conclusion
Since [tex]\((2, 3)\)[/tex] satisfies both equations, it is indeed a solution of the system.
Thus, the answer is: Yes.
### First Equation: [tex]\(2x - 4y = -8\)[/tex]
Substitute [tex]\(x = 2\)[/tex] and [tex]\(y = 3\)[/tex]:
[tex]\[ 2(2) - 4(3) = -8 \][/tex]
Calculate each term:
[tex]\[ 4 - 12 = -8 \][/tex]
Simplify:
[tex]\[ -8 = -8 \][/tex]
This holds true, so [tex]\((2, 3)\)[/tex] is a solution for the first equation.
### Second Equation: [tex]\(-3x + 5y = 9\)[/tex]
Substitute [tex]\(x = 2\)[/tex] and [tex]\(y = 3\)[/tex]:
[tex]\[ -3(2) + 5(3) = 9 \][/tex]
Calculate each term:
[tex]\[ -6 + 15 = 9 \][/tex]
Simplify:
[tex]\[ 9 = 9 \][/tex]
This also holds true, so [tex]\((2, 3)\)[/tex] is a solution for the second equation.
### Conclusion
Since [tex]\((2, 3)\)[/tex] satisfies both equations, it is indeed a solution of the system.
Thus, the answer is: Yes.
