Question

4x + 2y = 22
which variable should she choose to solve for so that she can use substitution to solve the system?
○ santa should solve for y in the second equation because the coefficients can be reduced by a common factor to eliminate the coefficient for y.
○ santa should solve for x in the first equation because the coefficients can be reduced by a common factor to eliminate the coefficient for x.
○ santa should solve for y in the first equation because the coefficients can be reduced by a common factor to eliminate the coefficient for y.
○ santa should solve for x in the second equation because the coefficients can be reduced by a common factor to eliminate the coefficient for x.

Explanation:

To determine the best variable for substitution, we analyze the given equation \(4x + 2y = 22\). For substitution, we want to solve for a variable with coefficients that have a common factor (to simplify). The coefficients of \(y\) are \(2\) (and the other terms: \(4x\) has coefficient \(4\), \(22\) is the constant). The coefficients \(4\), \(2\), and \(22\) have a common factor of \(2\) when solving for \(y\) (dividing the entire equation by \(2\) to isolate \(y\) is easier). Solving for \(y\) in the first (and only shown) equation: divide \(4x + 2y = 22\) by \(2\), we get \(2x + y = 11\), then \(y = 11 - 2x\), which is simple. The other options: solving for \(x\) in this equation would involve dividing by \(4\) (coefficients \(4\), \(2\), \(22\) have a common factor of \(2\), but dividing by \(4\) is less simple than dividing by \(2\) for \(y\)), and the options about second equation are incorrect as only one equation is shown (assuming the first equation here is \(4x + 2y = 22\)). So the correct option is the one where Santa solves for \(y\) in the first equation as coefficients can be reduced by a common factor (2) to eliminate \(y\)'s coefficient.

Answer:

Santa should solve for y in the first equation because the coefficients can be reduced by a common factor to eliminate the coefficient for y.