Which set of equations intersect at $$ (2,-1) ? $$ A. $$ \left\{\begin{array}{l}y=3+x \ y=-x+1\end{array} ight. $$ B. $$ \left\{\begin{array}{l}y=2 x-1 \ y=1-x\end{array} ight. $$ C. $$ \left\{\begin{array}{l}y=3 x \ y=2 x-1\end{array} ight. $$ D. $$ \left\{\begin{array}{l}y=2 x-5 \ y=1-x\end{array} ight. $$

Question

Which set of equations intersect at $$ (2,-1) ? $$ A. $$ \left\{\begin{array}{l}y=3+x \ y=-x+1\end{array}ight. $$ B. $$ \left\{\begin{array}{l}y=2 x-1 \ y=1-x\end{array}ight. $$ C. $$ \left\{\begin{array}{l}y=3 x \ y=2 x-1\end{array}ight. $$ D. $$ \left\{\begin{array}{l}y=2 x-5 \ y=1-x\end{array}ight. $$

UpStudy AI · Accepted Answer

Let's determine which set of equations has the point $$ (2, -1) $$ as their intersection.

**Option A:**
$$
\begin{cases}
y = x + 3 \
y = -x + 1
\end{cases}
$$
- Substitute $$ x = 2 $$ into the first equation: $$ y = 2 + 3 = 5 $$ (which is not $$-1$$).
  
**Option B:**
$$
\begin{cases}
y = 2x - 1 \
y = 1 - x
\end{cases}
$$
- Substitute $$ x = 2 $$ into the first equation: $$ y = 4 - 1 = 3 $$ (which is not $$-1$$).

**Option C:**
$$
\begin{cases}
y = 3x \
y = 2x - 1
\end{cases}
$$
- Substitute $$ x = 2 $$ into the first equation: $$ y = 6 $$ (which is not $$-1$$).

**Option D:**
$$
\begin{cases}
y = 2x - 5 \
y = 1 - x
\end{cases}
$$
- Substitute $$ x = 2 $$ into the first equation: $$ y = 4 - 5 = -1 $$.
- Substitute $$ x = 2 $$ into the second equation: $$ y = 1 - 2 = -1 $$.

Both equations in Option D are satisfied by the point $$ (2, -1) $$.

**Answer:** D
Option D intersects at $$ (2, -1) $$.

Which set of equations intersect at
A.
B.
C.
D.

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