Which of the following pairs of equations has exactly the same solution?(1 point)

Responses

−3.2x=0.64 and x/4=−0.05

3/8x=1 and 1/3 x=1/8

x/3.2=1.8 and 1.8x=3.2

−3/4 x=5/2 and 5/2x =−3/4

1 answer

To determine which pairs of equations have exactly the same solution, we can solve each one.

  1. For the first pair: \(-3.2x = 0.64\)

    To solve for \(x\): \[ x = \frac{0.64}{-3.2} = -0.2 \]

    Now for the second equation: \[ \frac{x}{4} = -0.05 \]

    Multiplying both sides by 4: \[ x = -0.2 \]

    Both equations have the solution \(x = -0.2\).

  2. For the second pair: \(\frac{3}{8}x = 1\)

    Multiplying both sides by \(\frac{8}{3}\): \[ x = \frac{8}{3} \]

    Now for the second equation: \(\frac{1}{3}x = \frac{1}{8}\)

    Multiplying both sides by 3: \[ x = \frac{3}{8} \]

    These equations do not have the same solution.

  3. For the third pair: \(\frac{x}{3.2} = 1.8\)

    Multiplying both sides by 3.2: \[ x = 1.8 \times 3.2 = 5.76 \]

    Now for the second equation: \(1.8x = 3.2\)

    Dividing both sides by 1.8: \[ x = \frac{3.2}{1.8} = \frac{16}{9} \approx 1.78 \]

    These equations do not have the same solution.

  4. For the fourth pair: \(-\frac{3}{4}x = \frac{5}{2}\)

    Multiplying both sides by -\(\frac{4}{3}\): \[ x = -\frac{4}{3} \times \frac{5}{2} = -\frac{10}{3} \]

    Now for the second equation: \(\frac{5}{2}x = -\frac{3}{4}\)

    Dividing both sides by \(\frac{5}{2}\): \[ x = -\frac{3}{4} \times \frac{2}{5} = -\frac{3}{10} \]

    These equations do not have the same solution.

From our work, the first pair of equations: \(-3.2x = 0.64\) and \(\frac{x}{4} = -0.05\)

are the only ones that have exactly the same solution, which is \(x = -0.2\).