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

Which equation can replace [tex]3x + 5y = 59[/tex] in the original system and still produce the same solution?

A. [tex]2x - y = -4[/tex]
B. [tex]10x - 5y = -20[/tex]
C. [tex]7x = 39[/tex]
D. [tex]13x = 39[/tex]



Answer :

GinnyAnswer
To determine which equation can replace [tex]\( 3x + 5y = 59 \)[/tex] in the original system while still producing the same solution, consider the original system of linear equations:

1. [tex]\( 3x + 5y = 59 \)[/tex]
2. [tex]\( 2x - y = -4 \)[/tex]

First, let's manipulate the second equation to align it with the first equation in a way that helps us maintain the solutions' consistency.

Multiply the second equation by 5:

[tex]\[ 5(2x - y) = 5(-4) \][/tex]

Expanding this, we get:

[tex]\[ 10x - 5y = -20 \][/tex]

Now, observe that the equation [tex]\( 10x - 5y = -20 \)[/tex] can serve as a replacement for the original equation [tex]\( 3x + 5y = 59 \)[/tex] while maintaining the solutions' consistency. This new system of equations will now be:

1. [tex]\( 10x - 5y = -20 \)[/tex]
2. [tex]\( 2x - y = -4 \)[/tex]

These two equations will yield the same solutions for [tex]\( x \)[/tex] and [tex]\( y \)[/tex] as the original system.

Therefore, the equivalent equation that can replace [tex]\( 3x + 5y = 59 \)[/tex] is [tex]\( 10x - 5y = -20 \)[/tex]. Hence, the correct option is:

[tex]\[ 10x - 5y = -20 \][/tex]

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