Question

1. match each equation in the first list to an equation in the second list that has the same solution.

a. $x = -3.2 + 1.6y$
b. $5x = 16 - 8y$ 1. $-5x - 8y = 16$
c. $x = \frac{16}{5} - \frac{8}{5}y$ 2. $-5x + 8y = 16$
d. $y = \frac{5}{8}x + 2$ 3. $5x + 8y = 16$
e. $y = \frac{16}{8} - 0.625x$
f. $-8y = 5x + 16$

Explanation:

Step1: Analyze Equation A ($x = -3.2 + 1.6y$)

Multiply both sides by 5 to eliminate decimals: $5x = -16 + 8y$. Rearrange to get $-5x + 8y = 16$, which matches Equation 2.

Step2: Analyze Equation B ($5x = 16 - 8y$)

Rearrange to $5x + 8y = 16$, which matches Equation 3.

Step3: Analyze Equation C ($x=\frac{16}{5}-\frac{8}{5}y$)

Multiply both sides by 5: $5x = 16 - 8y$, which is the same as Equation B, so it also matches Equation 3.

Step4: Analyze Equation D ($y=\frac{5}{8}x + 2$)

Multiply both sides by 8: $8y = 5x + 16$. Rearrange to $-5x + 8y = 16$? Wait, no: $8y - 5x = 16$ or $-5x + 8y = 16$? Wait, original equation: $y=\frac{5}{8}x + 2$. Multiply by 8: $8y = 5x + 16$. Then $-5x + 8y = 16$? Wait, no: $8y - 5x = 16$ is equivalent to $-5x + 8y = 16$, which is Equation 2? Wait, no, let's check again. Wait, $y=\frac{5}{8}x + 2$: multiply by 8: $8y = 5x + 16$. Then $-5x + 8y = 16$ (Equation 2). Wait, but earlier Equation A was $x = -3.2 + 1.6y$ which became $-5x + 8y = 16$ (Equation 2). Wait, maybe I made a mistake. Wait, Equation D: $y=\frac{5}{8}x + 2$. Let's solve for standard form. $y - \frac{5}{8}x = 2$. Multiply by 8: $8y - 5x = 16$ → $-5x + 8y = 16$ (Equation 2). So Equation D matches Equation 2. Wait, but Equation A also matched Equation 2. Let's check Equation A again: $x = -3.2 + 1.6y$. $-3.2$ is $-\frac{16}{5}$, $1.6$ is $\frac{8}{5}$. So $x = -\frac{16}{5} + \frac{8}{5}y$. Multiply by 5: $5x = -16 + 8y$ → $5x - 8y = -16$ → $-5x + 8y = 16$ (Equation 2). So Equation A and D both match Equation 2.

Step5: Analyze Equation E ($y=\frac{16}{8}-0.625x$)

Simplify: $y = 2 - 0.625x$. $0.625$ is $\frac{5}{8}$. So $y = 2 - \frac{5}{8}x$. Multiply by 8: $8y = 16 - 5x$ → $5x + 8y = 16$ (Equation 3).

Step6: Analyze Equation F ($-8y = 5x + 16$)

Rearrange: $5x + 8y = -16$? Wait, no: $-8y - 5x = 16$ → $5x + 8y = -16$? Wait, the right side is 16, left side is $-8y -5x = 16$ → $5x + 8y = -16$? But the options are 1: $-5x -8y = 16$ → $5x + 8y = -16$, which is the same as Equation F. So Equation F matches Equation 1.

Answer:

• A: 2. $-5x + 8y = 16$
• B: 3. $5x + 8y = 16$
• C: 3. $5x + 8y = 16$
• D: 2. $-5x + 8y = 16$
• E: 3. $5x + 8y = 16$
• F: 1. $-5x - 8y = 16$