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3.

3x + 8y = 16
8 = 3x+8y
y=10-22
6x + 3y = 30
2x + 3y = 5
x = -2y
No Solution
One Solution
Infinitely Many Solutions

User Sbp
by
8.9k points

1 Answer

5 votes

Final answer:

To solve the given system of equations, we can use the method of elimination. After eliminating the variable y, we find that x = 16/3 and y = 0, which gives us one solution. Therefore, the answer is One Solution.

Step-by-step explanation:

The given system of equations is as follows:

3x + 8y = 16

6x + 3y = 30

2x + 3y = 5

To solve this system, we can use the method of elimination. We'll eliminate the variable y by multiplying the equations. We can multiply the first equation by 3 and the second equation by 8 in order to get the same coefficients for y:

9x + 24y = 48

48x + 24y = 240

We can subtract the two equations to eliminate y:

(48x + 24y) - (9x + 24y) = 240 - 48

Simplifying this, we get:

39x = 192

Dividing by 39, we find that x = 192/39 = 16/3.

Now, substituting this value of x into any of the original equations, we can solve for y. Let's substitute it into the first equation:

3(16/3) + 8y = 16

16 + 8y = 16

8y = 0

y = 0

So, the solution to the system of equations is x = 16/3 and y = 0.

Since there is only one solution to the system, the answer is One Solution.

User Jangari
by
8.1k points

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