Questions: Choose the most appropriate method for solving the system of equations. Do not solve. x+y=2070 3x+4y=8570 Substitution Addition

Choose the most appropriate method for solving the system of equations. Do not solve. x+y=2070 3x+4y=8570 Substitution Addition
Transcript text: Choose the most appropriate method for solving the system of equations. Do not solve. \[ \begin{array}{c} x+y=2070 \\ 3 x+4 y=8570 \end{array} \] Substitution Addition
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Solution

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Solution Steps

To determine the most appropriate method for solving the given system of equations, we should consider the structure of the equations. The first equation is simple and can be easily solved for one variable in terms of the other, making substitution a straightforward choice. However, the coefficients in the second equation suggest that elimination (addition) might also be efficient. Since the question asks for the most appropriate method, substitution is often preferred when one equation is already solved for a variable or can be easily manipulated to do so.

Step 1: Express \( x \) in terms of \( y \)

From the first equation \( x + y = 2070 \), we can express \( x \) in terms of \( y \): \[ x = 2070 - y \]

Step 2: Substitute \( x \) in the second equation

Substitute the expression for \( x \) from Step 1 into the second equation \( 3x + 4y = 8570 \): \[ 3(2070 - y) + 4y = 8570 \]

Step 3: Simplify and solve for \( y \)

Simplify the equation: \[ 6210 - 3y + 4y = 8570 \] \[ 6210 + y = 8570 \] Subtract 6210 from both sides: \[ y = 8570 - 6210 \] \[ y = 2360 \]

Final Answer

The value of \( y \) is \(\boxed{2360}\).

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