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

Question

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

Answer 1

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 $x=-0.2$.