Answered

Westonci.ca is the Q&A platform that connects you with experts who provide accurate and detailed answers. Get quick and reliable solutions to your questions from a community of seasoned experts on our user-friendly platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

Given the system of equations:
[tex]\[
3x + 4y = 18, \quad y = \frac{3}{2} x
\][/tex]

Which of the following ordered pairs [tex]\((x, y)\)[/tex] is a solution of the system of equations above?

A. [tex]\((2, 3)\)[/tex]

B. [tex]\((3, 2.25)\)[/tex]

C. [tex]\((4, 1.5)\)[/tex]

D. [tex]\((4, 6)\)[/tex]

Sagot :

GinnyAnswer
To determine which ordered pair [tex]\((x, y)\)[/tex] is a solution to the system of equations:
[tex]\[ 3x + 4y = 18 \][/tex]
[tex]\[ y = \frac{3}{2}x \][/tex]

We will check each option to see if it satisfies both equations.

### Option A: [tex]\((2, 3)\)[/tex]

1. Plug [tex]\(x = 2\)[/tex] and [tex]\(y = 3\)[/tex] into the first equation:
[tex]\[ 3(2) + 4(3) = 6 + 12 = 18 \][/tex]
This satisfies the first equation.

2. Check the second equation with [tex]\(x = 2\)[/tex] and [tex]\(y = 3\)[/tex]:
[tex]\[ y = \frac{3}{2}(2) = 3 \][/tex]
This satisfies the second equation.

Since [tex]\((2, 3)\)[/tex] satisfies both equations, [tex]\((2, 3)\)[/tex] is a solution to the system.

### Option B: [tex]\((3, 2.25)\)[/tex]

1. Plug [tex]\(x = 3\)[/tex] and [tex]\(y = 2.25\)[/tex] into the first equation:
[tex]\[ 3(3) + 4(2.25) = 9 + 9 = 18 \][/tex]
This satisfies the first equation.

2. Check the second equation with [tex]\(x = 3\)[/tex] and [tex]\(y = 2.25\)[/tex]:
[tex]\[ y = \frac{3}{2}(3) = 4.5 \][/tex]
This does not satisfy the second equation since [tex]\(2.25 \neq 4.5\)[/tex].

Since [tex]\((3, 2.25)\)[/tex] does not satisfy both equations, it is not a solution to the system.

### Option C: [tex]\((4, 1.5)\)[/tex]

1. Plug [tex]\(x = 4\)[/tex] and [tex]\(y = 1.5\)[/tex] into the first equation:
[tex]\[ 3(4) + 4(1.5) = 12 + 6 = 18 \][/tex]
This satisfies the first equation.

2. Check the second equation with [tex]\(x = 4\)[/tex] and [tex]\(y = 1.5\)[/tex]:
[tex]\[ y = \frac{3}{2}(4) = 6 \][/tex]
This does not satisfy the second equation since [tex]\(1.5 \neq 6\)[/tex].

Since [tex]\((4, 1.5)\)[/tex] does not satisfy both equations, it is not a solution to the system.

### Option D: [tex]\((4, 6)\)[/tex]

1. Plug [tex]\(x = 4\)[/tex] and [tex]\(y = 6\)[/tex] into the first equation:
[tex]\[ 3(4) + 4(6) = 12 + 24 = 36 \][/tex]
This does not satisfy the first equation since [tex]\(36 \neq 18\)[/tex].

2. Check the second equation with [tex]\(x = 4\)[/tex] and [tex]\(y = 6\)[/tex]:
[tex]\[ y = \frac{3}{2}(4) = 6 \][/tex]
This satisfies the second equation.

Since [tex]\((4, 6)\)[/tex] does not satisfy both equations, it is not a solution to the system.

### Conclusion

The ordered pair [tex]\((2, 3)\)[/tex] satisfies both equations in the system. Therefore, the solution to the system of equations [tex]\[ 3x + 4y = 18 \][/tex] and [tex]\[ y = \frac{3}{2}x \][/tex] is:

A. [tex]\((2, 3)\)[/tex]
Thank you for choosing our service. We're dedicated to providing the best answers for all your questions. Visit us again. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.