To solve the system of equations using substitution, we start with the two equations:
- \( 3x + 2y = 15 \)
- \( y = 6x \)
We can substitute the expression for \( y \) from the second equation into the first equation.
Substituting \( y = 6x \) into \( 3x + 2y = 15 \):
\[ 3x + 2(6x) = 15 \]
Now simplify the equation:
\[ 3x + 12x = 15 \] \[ 15x = 15 \]
Next, divide both sides by 15 to solve for \( x \):
\[ x = 1 \]
Now that we have \( x \), we can substitute it back into the equation \( y = 6x \) to find \( y \):
\[ y = 6(1) = 6 \]
Thus, the solution to the system of equations is:
\[ (x, y) = (1, 6) \]
So the final answer is:
\[ \boxed{(1, 6)} \]
3 answers