Question
Sarita has to solve the problem below for homework.
2 x + 3 y = 25. 4+ 2 y = 22.
Which variable should she choose to solve for so that she can use substitution to solve the system?
Sarita should solve for y in the second equation because the coefficients can be reduced by a common factor to eliminate the coefficient for y.
Sarita should solve for x in the first equation because the coefficients can be reduced by a common factor to eliminate the coefficient for x.
Sarita should solve for y in the first equation because the coefficients can be reduced by a common factor to eliminate the coefficient for y.
Sarita should solve for x in the second equation because the coefficients can be reduced by a common factor to eliminate the coefficient for x.
2 x + 3 y = 25. 4+ 2 y = 22.
Which variable should she choose to solve for so that she can use substitution to solve the system?
Sarita should solve for y in the second equation because the coefficients can be reduced by a common factor to eliminate the coefficient for y.
Sarita should solve for x in the first equation because the coefficients can be reduced by a common factor to eliminate the coefficient for x.
Sarita should solve for y in the first equation because the coefficients can be reduced by a common factor to eliminate the coefficient for y.
Sarita should solve for x in the second equation because the coefficients can be reduced by a common factor to eliminate the coefficient for x.
Answers
GPT-4o mini
To determine which variable Sarita should solve for to use substitution efficiently, let's first look at the given equations:
1. \( 2x + 3y = 25 \)
2. \( 4 + 2y = 22 \)
We can simplify the second equation first:
\[
2y = 22 - 4
\]
\[
2y = 18
\]
\[
y = 9
\]
At this point, we have solved for \(y\) directly, but if we rearrange the second equation instead, we find that:
\[
2y = 22 - 4
\]
\[
2y = 18
\]
\[
y = 9
\]
If we substitute \(y = 9\) back into the first equation to find \(x\):
\[
2x + 3(9) = 25
\]
\[
2x + 27 = 25
\]
\[
2x = 25 - 27
\]
\[
2x = -2
\]
\[
x = -1
\]
Now to determine which approach to take; if we see how the second equation can be simplified, we can see \(2y = 18\) allows us to solve directly for \(y\). The coefficients do simplify, and we can deduce from this.
Now we reconsider the options given:
1. **Solve for \(y\) in the second equation**: Yes, can be simplified directly.
2. **Solve for \(x\) in the first equation**: Not as straightforward compared to solving for \(y\).
3. **Solve for \(y\) in the first equation**: Possible but involves larger steps.
4. **Solve for \(x\) in the second equation**: Not applicable, as it does not include \(x\).
Thus, the best choice for Sarita is to **solve for \(y\) in the second equation** since it simplifies directly, making substitution easy.
**Final Answer**: Sarita should solve for \(y\) in the second equation because the coefficients can be reduced by a common factor to eliminate the coefficient for \(y\).
1. \( 2x + 3y = 25 \)
2. \( 4 + 2y = 22 \)
We can simplify the second equation first:
\[
2y = 22 - 4
\]
\[
2y = 18
\]
\[
y = 9
\]
At this point, we have solved for \(y\) directly, but if we rearrange the second equation instead, we find that:
\[
2y = 22 - 4
\]
\[
2y = 18
\]
\[
y = 9
\]
If we substitute \(y = 9\) back into the first equation to find \(x\):
\[
2x + 3(9) = 25
\]
\[
2x + 27 = 25
\]
\[
2x = 25 - 27
\]
\[
2x = -2
\]
\[
x = -1
\]
Now to determine which approach to take; if we see how the second equation can be simplified, we can see \(2y = 18\) allows us to solve directly for \(y\). The coefficients do simplify, and we can deduce from this.
Now we reconsider the options given:
1. **Solve for \(y\) in the second equation**: Yes, can be simplified directly.
2. **Solve for \(x\) in the first equation**: Not as straightforward compared to solving for \(y\).
3. **Solve for \(y\) in the first equation**: Possible but involves larger steps.
4. **Solve for \(x\) in the second equation**: Not applicable, as it does not include \(x\).
Thus, the best choice for Sarita is to **solve for \(y\) in the second equation** since it simplifies directly, making substitution easy.
**Final Answer**: Sarita should solve for \(y\) in the second equation because the coefficients can be reduced by a common factor to eliminate the coefficient for \(y\).