10. Solve using substitution: $$ \quad y=4 x+2 \quad 6 x-y=10 $$ $$ y=4(6 x-2=10)+2 $$

Question

UpStudy AI · Accepted Answer

To solve the system of equations using the **substitution method**, follow these steps:

$$
\begin{cases}
y = 4x + 2 \quad \text{(Equation 1)} \
6x - y = 10 \quad \text{(Equation 2)}
\end{cases}
$$

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

Equation 1 is already solved for $$ y $$:
$$
y = 4x + 2
$$

### Step 2: Substitute the expression from Step 1 into the other equation

Substitute $$ y = 4x + 2 $$ into Equation 2:
$$
6x - (4x + 2) = 10
$$

### Step 3: Simplify and solve for $$ x $$

$$
6x - 4x - 2 = 10 \
2x - 2 = 10 \
2x = 10 + 2 \
2x = 12 \
x = \frac{12}{2} \
x = 6
$$

### Step 4: Substitute the value of $$ x $$ back into one of the original equations to find $$ y $$

Using Equation 1:
$$
y = 4x + 2 \
y = 4(6) + 2 \
y = 24 + 2 \
y = 26
$$

### Solution

$$
x = 6 \
y = 26
$$

**Therefore, the solution to the system is $$ x = 6 $$ and $$ y = 26 $$.**
The solution is $$ x = 6 $$ and $$ y = 26 $$.

10. Solve using substitution: \( \quad y=4 x+2 \quad 6 x-y=10 \) \[ y=4(6 x-2=10)+2 \]