Final answer:
The system of equations x + 4y = 9 and 4x + 5y = 3 was solved using the addition method to find that the solution is x = -3 and y = 3.
Step-by-step explanation:
To solve the system of equations by the addition method, we first need to manipulate the equations to eliminate one variable. We have the following two equations:
We can eliminate x by multiplying the first equation by -4 and adding it to the second equation.
-4(x + 4y) = -4(9)
-4x - 16y = -36
Now add this new equation to the second equation in the original system:
(-4x - 16y) + (4x + 5y) = -36 + 3
-11y = -33
Divide both sides by -11 to solve for y:
y = 3
Now we substitute y = 3 into the first original equation:
x + 4(3) = 9
x + 12 = 9
Subtract 12 from both sides to solve for x:
x = -3
Our solution for the system using the addition method is x = -3 and y = 3.