3. A student attempted to solve the system of equations and has made an srror in the finst step. Identify the error and explain what the student needs to do to correct il. $$ \left\{\begin{array}{c}x=y-7 \ 3 x+15 y=-1\end{array} ight. $$ Student's first step: $$ 3 x+15(y-7)=-1 $$

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3. A student attempted to solve the system of equations and has made an srror in the finst step. Identify the error and explain what the student needs to do to correct il. $$ \left\{\begin{array}{c}x=y-7 \ 3 x+15 y=-1\end{array}ight. $$ Student's first step: $$ 3 x+15(y-7)=-1 $$

UpStudy AI · Accepted Answer

The student has incorrectly substituted into the second equation. The original system is

$$
\begin{cases}
x = y - 7, \
3x + 15y = -1.
\end{cases}
$$

Since $$ x = y - 7 $$, the correct substitution into the second equation should be to replace $$ x $$ with $$ y - 7 $$ in the term $$ 3x $$ only. This yields

$$
3(y-7) + 15y = -1.
$$

However, the student replaced the wrong term and wrote

$$
3x + 15(y-7) = -1,
$$

which mistakenly substituted $$ y-7 $$ for $$ y $$ in the second term instead of substituting for $$ x $$ in the first term.

To correct the mistake, the student must substitute $$ x = y-7 $$ into every instance of $$ x $$ in the equation, not into $$ y $$. Thus, the student should start with

$$
3(y-7)+15y=-1.
$$
The student incorrectly substituted $$ y-7 $$ into the second term of the second equation instead of substituting $$ x = y - 7 $$ into the first term. To correct this, the student should replace every $$ x $$ in the second equation with $$ y - 7 $$, resulting in $$ 3(y - 7) + 15y = -1 $$.

3. A student attempted to solve the system of equations and has made an srror in the finst step. Identify the error and explain what the student needs to do to correct il. \( \left\{\begin{array}{c}x=y-7 \\ 3 x+15 y=-1\end{array}\right. \) Student's first step: \( 3 x+15(y-7)=-1 \)

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