What is the solution of this system of equations? $$ \left\{\begin{array}{l}x-4 y=7 \ 2 x+y=5\end{array} ight. $$

Question

What is the solution of this system of equations? $$ \left\{\begin{array}{l}x-4 y=7 \ 2 x+y=5\end{array}ight. $$

UpStudy AI · Accepted Answer

To solve the system of equations:

$$
\begin{cases}
x - 4y = 7 \
2x + y = 5
\end{cases}
$$

**Step 1: Solve the first equation for $$ x $$.**

$$
x - 4y = 7 \
\Rightarrow x = 7 + 4y
$$

**Step 2: Substitute $$ x = 7 + 4y $$ into the second equation.**

$$
2x + y = 5 \
2(7 + 4y) + y = 5 \
14 + 8y + y = 5 \
14 + 9y = 5
$$

**Step 3: Solve for $$ y $$.**

$$
9y = 5 - 14 \
9y = -9 \
y = -1
$$

**Step 4: Substitute $$ y = -1 $$ back into the expression for $$ x $$.**

$$
x = 7 + 4(-1) \
x = 7 - 4 \
x = 3
$$

**Solution:**
$$
x = 3 \
y = -1
$$

**Verification:**

Plugging $$ x = 3 $$ and $$ y = -1 $$ into both original equations:

1. $$ 3 - 4(-1) = 3 + 4 = 7 $$ ✔️
2. $$ 2(3) + (-1) = 6 - 1 = 5 $$ ✔️

Both equations are satisfied, confirming the solution is correct.

**Final Answer:**
The solution is $$ x = 3 $$ and $$ y = -1 $$.
The solution is $$ x = 3 $$ and $$ y = -1 $$.

What is the solution of this system of equations? \( \left\{\begin{array}{l}x-4 y=7 \\ 2 x+y=5\end{array}\right. \)