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Ita worked to solve a system of equations.

[tex]\[ \begin{array}{c} 4x + y = -5 \\ x - y = -5 \end{array} \][/tex]

Step 1: ???
Step 2: \( x = -2 \)
Step 3: \( 4(-2) + y = -5 \)
Step 4: \( -8 + y = -5 \)
Step 5: \( y = 3 \)

Berta determined that the solution is \((-2, 3)\).

Which could have been the equation Berta found in Step 1?

A. \( 4x = 0 \)
B. \( 5x = 10 \)
C. \( 5x = -10 \)
D. [tex]\( 5x = -25 \)[/tex]



Answer :

GinnyAnswer
To solve the given system of equations and determine which equation Berta found in step 1, let's proceed with a detailed, step-by-step solution:

Given the system of equations:
1. \( 4x + y = -5 \)
2. \( x - y = -5 \)

Step 1: Isolate \( y \) in the second equation
[tex]\[ x - y = -5 \][/tex]
[tex]\[ y = x + 5 \][/tex]

Step 2: Substitute \( y = x + 5 \) from the second equation into the first equation
[tex]\[ 4x + (x + 5) = -5 \][/tex]
This simplifies to:
[tex]\[ 4x + x + 5 = -5 \][/tex]
[tex]\[ 5x + 5 = -5 \][/tex]

Step 3: Solve for \( x \)
[tex]\[ 5x + 5 = -5 \][/tex]
Subtract 5 from both sides:
[tex]\[ 5x = -10 \][/tex]
Divide both sides by 5:
[tex]\[ x = -2 \][/tex]

Step 4: Substitute \( x = -2 \) back into the expression for \( y \)
[tex]\[ y = x + 5 \][/tex]
[tex]\[ y = -2 + 5 \][/tex]
[tex]\[ y = 3 \][/tex]

Berta determined that the solution is \((-2, 3)\). Therefore, the equation found in step 1 could have been:
[tex]\[ 5x = -10 \][/tex]

The correct choice from the given options is:
[tex]\[ 5x = -10 \][/tex]

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