Question

Which system of equations has the same solution as the system below?
2, x, plus, 2, y, equals, 30
2x+2y=
30
3, x, plus, 4, y, equals, 55
3x+4y=
55
Answer
Multiple Choice Answers
minus, 4, x, plus, 2, y, equals, minus, 60−4x+2y=−60
3, x, plus, 4, y, equals, 553x+4y=55
minus, 4, x, minus, 4, y, equals, 30−4x−4y=30
3, x, plus, 4, y, equals, 553x+4y=55
minus, 4, x, minus, 4, y, equals, minus, 60−4x−4y=−60
3, x, plus, 4, y, equals, 553x+4y=55
2, x, minus, 4, y, equals, minus, 602x−4y=−60
3, x, plus, 4, y, equals, 553x+4y=55

Answer 1

To find a system of equations that has the same solution as the given system, we can manipulate the equations while maintaining their equivalence.

The original system is:
1. \(2x + 2y = 30\)
2. \(3x + 4y = 55\)

To verify each option, we can check if we can derive it from the original equations.

Let's simplify:

1. The first equation \(2x + 2y = 30\) can be divided by 2:
\[
x + y = 15 \quad \text{(this equation is equivalent)}
\]

2. The second equation \(3x + 4y = 55\) is already in its simplest form.

Now, let's analyze the options given:

- **Option A**: \(-4x + 2y = -60\)

To check if this is equivalent, we can multiply the original equation. If we multiply the first equation by -2, we would get \(-4x - 4y = -60\), which doesn't match.

- **Option B**: \(3x + 4y = 55\)

This one is identical to the original second equation. So it is equivalent.

- **Option C**: \(-4x - 4y = 30\)

This does not derive from the original equations when multiplied or modified.

- **Option D**: \(2x - 4y = -60\)

Dividing doesn't lead to equivalency as per our initial equations.

- **Option E**: \(3x + 4y = 55\) (repeat)

Again, this one is identical to the original second equation.

- **Option F**: \( -4x - 4y = -60 \)

This doesn’t produce equivalency based on our manipulations.

- **Option G**: \(2x - 4y = -60\)

Also does not yield equivalent results.

Thus, the correct answer is:
**3. \(3x + 4y = 55\)**.
This is identical to the second equation of the original system.