Final answer:
To solve the system of equations using the substitution method, solve one equation for one variable and substitute that expression into the other equation. The solution to the system of equations is x = -2 and y = 1.
Step-by-step explanation:
To solve the system of equations using the substitution method, we need to solve one equation for one variable and substitute that expression into the other equation. Let's start by solving the first equation for y:
y = 3x + 7
Next, we substitute this value of y into the second equation:
4x + 9(3x + 7) = 1
Distribute the 9 into the parentheses:
4x + 27x + 63 = 1
Combine like terms:
31x + 63 = 1
Subtract 63 from both sides:
31x = -62
Divide both sides by 31:
x = -2
Substitute this value of x back into the first equation to solve for y:
y = 3(-2) + 7
y = 1
So the solution to the system of equations is x = -2 and y = 1.