Answered

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Is [tex]\((2,3)\)[/tex] a solution of the system [tex]\(2x - 4y = -8\)[/tex] and [tex]\(-3x + 5y = 9\)[/tex]?

A. Not enough information is given to determine this.
B. Yes
C. [tex]\((2,3)\)[/tex] is a solution in one equation, but not both.
D. No

Sagot :

GinnyAnswer
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.
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