The system of equations can be solved using linear combination to eliminate one of the variables.

Question

2x − y = −4 → 10x − 5y = −20
3x + 5y = 59 → 3x + 5y = 59
13x = 39
Which equation can replace 3x + 5y = 59 in the original system and still produce the same solution?

2x – y = –4
10x – 5y = –20
7x = 39
13x = 39

Answer 1

To determine which equation can replace \(3x + 5y = 59\) in the original system while still producing the same solution, we will first solve the original system of equations.

The given equations are:

1. \(2x - y = -4\)
2. \(3x + 5y = 59\)

Step 1: Solve for \(y\) from the first equation

From \(2x - y = -4\):

\[ y = 2x + 4 \]

Step 2: Substitute \(y\) into the second equation

Substituting \(y\) into \(3x + 5y = 59\):

\[ 3x + 5(2x + 4) = 59 \] \[ 3x + 10x + 20 = 59 \] \[ 13x + 20 = 59 \] Subtracting 20 from both sides: \[ 13x = 39 \]

Step 3: Determine the replacement equation

We see that \(13x = 39\) is derived from the original system. Thus, \(13x = 39\) can replace \(3x + 5y = 59\) in the original system while still producing the same solution.

Conclusion

The equation that can replace \(3x + 5y = 59\) is:

\[ 13x = 39 \]

This is the correct answer.