To identify which variable will be eliminated, you can work with the given system of linear equations:
[tex]\[ 5x - 4y = 11 \][/tex]
[tex]\[ 5x + 4y = -14 \][/tex]
To eliminate a variable, we can add or subtract these two equations. Let's add them:
[tex]\[ (5x - 4y) + (5x + 4y) = 11 + (-14) \][/tex]
When we add these equations, the [tex]\(-4y\)[/tex] and [tex]\(+4y\)[/tex] terms cancel each other out:
[tex]\[ 5x + 5x - 4y + 4y = 11 - 14 \][/tex]
This simplifies to:
[tex]\[ 10x = -3 \][/tex]
As you can see, the variable [tex]\(y\)[/tex] gets eliminated, and we are left with an equation involving only [tex]\(x\)[/tex]:
[tex]\[ 10x = -3 \][/tex]
Thus, the variable that will be eliminated is:
[tex]\[ y \][/tex]\
