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

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UpStudy AI · Accepted 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**.
The value of $$ y $$ is $$-17$$.

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