To solve the system of equations using the substitution method, we start with the two given equations:
1) [tex]\( y = 5x \)[/tex]
2) [tex]\( 3x + 16 = y \)[/tex]
### Step-by-Step Solution:
#### Step 1: Substitute [tex]\( y \)[/tex] from the first equation into the second equation
We know from the first equation that [tex]\( y = 5x \)[/tex]. We can substitute this expression for [tex]\( y \)[/tex] in the second equation:
[tex]\[ 3x + 16 = 5x \][/tex]
#### Step 2: Solve for [tex]\( x \)[/tex]
Now, we need to isolate [tex]\( x \)[/tex] on one side of the equation. We start by moving the [tex]\( 3x \)[/tex] term to the other side:
[tex]\[ 16 = 5x - 3x \][/tex]
Simplify the equation:
[tex]\[ 16 = 2x \][/tex]
To solve for [tex]\( x \)[/tex], we divide both sides by 2:
[tex]\[ x = \frac{16}{2} \][/tex]
[tex]\[ x = 8 \][/tex]
So, the value of [tex]\( x \)[/tex] is [tex]\( x = 8 \)[/tex].
#### Step 3: Substitute [tex]\( x \)[/tex] back into the first equation to find [tex]\( y \)[/tex]
We use the value of [tex]\( x \)[/tex] we just found and substitute it back into the first equation [tex]\( y = 5x \)[/tex]:
[tex]\[ y = 5 \cdot 8 \][/tex]
[tex]\[ y = 40 \][/tex]
So, the value of [tex]\( y \)[/tex] is [tex]\( y = 40 \)[/tex].
#### Conclusion
The solution to the system of equations is:
[tex]\[ (x, y) = (8, 40) \][/tex]
Thus, the point [tex]\((8, 40)\)[/tex] satisfies both original equations.
