Solve the system by substitution. $$ \begin{aligned} x & =-4 y+6 \ 2 x+9 y & =16\end{aligned} $$

Question

UpStudy AI · Accepted Answer

To solve the system of equations by substitution:

$$
\begin{aligned}
x &= -4y + 6 \quad \text{(1)} \
2x + 9y &= 16 \quad \text{(2)}
\end{aligned}
$$

**Step 1: Substitute Equation (1) into Equation (2)**

Since Equation (1) gives $$ x $$ in terms of $$ y $$, we can substitute $$ x = -4y + 6 $$ into Equation (2):

$$
2(-4y + 6) + 9y = 16
$$

**Step 2: Expand and Simplify**

$$
-8y + 12 + 9y = 16
$$

Combine like terms:

$$
( -8y + 9y ) + 12 = 16 \
y + 12 = 16
$$

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

$$
y = 16 - 12 \
y = 4
$$

**Step 4: Substitute $$ y = 4 $$ back into Equation (1) to find $$ x $$**

$$
x = -4(4) + 6 \
x = -16 + 6 \
x = -10
$$

**Solution:**

$$
x = -10 \
y = 4
$$
$$ x = -10 $$ and $$ y = 4 $$.

Solve the system by substitution. \[ \begin{aligned} x & =-4 y+6 \\ 2 x+9 y & =16\end{aligned} \]