Ask AI: Solve the following system of equations
6x+5y=-10 3x+5y=20

Question

Solve the following system of equations
6x+5y=-10   3x+5y=20

gpt-4.1 · Accepted Answer

Let's solve the given system step by step:

The system is:

$$
\begin{cases}
6x + 5y = -10 \
3x + 5y = 20
\end{cases}
$$

### Step 1: Eliminate one variable

Subtract the second equation from the first to eliminate $y$:

$$
(6x + 5y) - (3x + 5y) = -10 - 20
$$
$$
6x - 3x + 5y - 5y = -30
$$
$$
3x = -30
$$

### Step 2: Solve for $x$

$$
3x = -30 \implies x = \frac{-30}{3} = -10
$$

### Step 3: Substitute $x$ into one of the original equations

Let's use the second equation:

$$
3x + 5y = 20
$$
$$
3(-10) + 5y = 20
$$
$$
-30 + 5y = 20
$$
$$
5y = 20 + 30 = 50
$$
$$
y = \frac{50}{5} = 10
$$

### Final Answer:

$$
\boxed{x = -10, \quad y = 10}
$$

Ask AI on The Internet