Solve Linear Equation: Finding Values for △ and ☐ in 6.1x + 7.4y Expression

To solve this equation, we need to equate the coefficients of the terms involving $x$, $y$, and constants on both sides of the equation:

• On the left-hand side (LHS), the expression is $\triangle + 6.1x + 7.4y + \square$.
• On the right-hand side (RHS), the expression is $4.7x - 0.4y$.

1. Balancing $x$ coefficients:
Compare the coefficients of the terms involving $x$:

• From LHS: $6.1$.
• From RHS: $4.7$.

To make the coefficients equal:

$6.1x + \square_x = 4.7x$ → $\square_x = 4.7x - 6.1x = -1.4x$.

2. Balancing $y$ coefficients:
Compare the coefficients of the terms involving $y$:

• From LHS: $7.4$.
• From RHS: $-0.4$.

To make the coefficients equal:

$7.4y + \triangle_y = -0.4y$ → $\triangle_y = -0.4y - 7.4y = -7.8y$.

3. Constant terms:
There are no constant terms explicitly present on either side, so no adjustment is needed for constants.

Now verify the answer choices using $\triangle = -7.8y$ and $\square = -1.4x$:

• Choice a: $\triangle=-7y$, $\square=-1.4x$ — Not correct as $\triangle=-7.8y$.
• Choice b: $\triangle=-7.8y$, $\square=-1.4x$ — Correct.
• Choice c: $\triangle=-1.4x$, $\square=-7.8y$ — Correct as they match reversed because the positions are not fixed.
• Choice d: $\triangle=-3.4x$, $\square=-7.8y+2x$ — Correctly matches based on $\triangle=-3.4x$ as the sum effects result in $-7.8y+2x$.

The correct answer to the problem is b, c, d.