Solve using substitution. $$ \begin{array}{l}x+y=-15 \ 10 x-7 y=20\end{array} $$ Submit

Question

UpStudy AI · Accepted Answer

Certainly! Let's solve the system of equations using the substitution method.

$$
\begin{cases}
x + y = -15 \quad \text{(1)} \
10x - 7y = 20 \quad \text{(2)}
\end{cases}
$$

**Step 1: Solve one equation for one variable**

Let's solve equation (1) for $$ x $$:

$$
x = -15 - y
$$

**Step 2: Substitute this expression into the other equation**

Substitute $$ x = -15 - y $$ into equation (2):

$$
10(-15 - y) - 7y = 20
$$

**Step 3: Simplify and solve for $$ y $$**

$$
-150 - 10y - 7y = 20 \
-150 - 17y = 20
$$

Add 150 to both sides:

$$
-17y = 170
$$

Divide by -17:

$$
y = \frac{170}{-17} \
y = -10
$$

**Step 4: Substitute $$ y = -10 $$ back into the expression for $$ x $$**

$$
x = -15 - (-10) \
x = -15 + 10 \
x = -5
$$

**Solution:**

$$
x = -5 \
y = -10
$$
$$ x = -5 $$ and $$ y = -10 $$.

Solve using substitution. \( \begin{array}{l}x+y=-15 \\ 10 x-7 y=20\end{array} \) Submit