Question

What is the solution of the system of equations:

3x + 2y = 8
5x + 2y = 12
a) (2, 4)
b) (-2, 7)
c) (43, 2)
d) (2, 1)

Answer 1

The solution to the system of equations '3x + 2y = 8' and '5x + 2y = 12' is found using the subtraction method, leading to x=2 and y=1. The answer is option (d) (2, 1).

Step-by-step explanation:

The student is asking for the solution to a system of linear equations:

• 3x + 2y = 8
• 5x + 2y = 12

To solve for the values of x and y, we will use the method of subtraction. First, let's subtract the second equation from the first:

3x + 2y = 8
-(5x + 2y = 12)
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-2x = -4
Solving for x, we get:

x = 2
Now that we have x, we can substitute it into one of the original equations to solve for y. Using the first equation:

3(2) + 2y = 8
6 + 2y = 8
2y = 2
y = 1

Therefore, the correct answer is:

x = 2, y = 1

Which corresponds to option (d) (2, 1).