2:21 PM Wed Feb 19 68\% kanawha.schoology.com 514 HS ALGEBRA II_3072_02000000: 16 Quiz: Systems of Equations (Remote Learning Day) Submissions Enabled Grade: N/A This test/quiz is accepting submissions until Wednesday, February 19, 2025 at 3:00 pm Question 4 of \( 6 \mid \) Page 4 of 6 Question 4 (1 point) \[ \begin{array}{c} x+y=29 \\ x+2 y=12 \end{array} \] - If the ordered pair \( (x, y) \) is the solution to the system of equations above, what is the value of \( y \) ? A) -17 B) 12 C) 46 D) 75 \( a \quad A \) b \( B \) c \( C \) d \( D \) Next Page Once you click Next Page you will not be able to change your answer

Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}x+y=29\\x+2y=12\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}x=29-y\\x+2y=12\end{array}\right.\) - step2: Substitute the value of \(x:\) \(29-y+2y=12\) - step3: Add the terms: \(29+y=12\) - step4: Move the constant to the right side: \(y=12-29\) - step5: Subtract the numbers: \(y=-17\) - step6: Substitute the value of \(y:\) \(x=29-\left(-17\right)\) - step7: Substitute back: \(x=29+17\) - step8: Calculate: \(x=46\) - step9: Calculate: \(\left\{ \begin{array}{l}x=46\\y=-17\end{array}\right.\) - step10: Check the solution: \(\left\{ \begin{array}{l}x=46\\y=-17\end{array}\right.\) - step11: Rewrite: \(\left(x,y\right) = \left(46,-17\right)\) To solve the system of equations: \[ \begin{array}{c} x + y = 29 \\ x + 2y = 12 \end{array} \] we can find the values of \(x\) and \(y\). 1. From the first equation, we can express \(x\) in terms of \(y\): \[ x = 29 - y \] 2. Substitute \(x\) into the second equation: \[ (29 - y) + 2y = 12 \] 3. Simplify the equation: \[ 29 - y + 2y = 12 \\ 29 + y = 12 \] 4. Solve for \(y\): \[ y = 12 - 29 \\ y = -17 \] Now that we have \(y = -17\), we can also find \(x\) using the first equation: \[ x + (-17) = 29 \\ x = 29 + 17 \\ x = 46 \] Thus, the ordered pair \((x, y)\) is \((46, -17)\). The value of \(y\) is \(-17\). The correct answer is: **A) -17**.