Final answer:
To solve the system of equations, we can use the substitution method. Substituting one equation into the other, we can find the values of x and y that satisfy both equations simultaneously.
Step-by-step explanation:
To solve the system of equations using substitution or elimination, we need to find the values of x and y that satisfy both equations simultaneously. Let's use the substitution method:
Start with the equation y = -4x + 9.
Substitute this expression for y into the second equation: -4x + 9 = 3x - 5.
Add 4x to both sides: 9 = 7x - 5.
Add 5 to both sides: 14 = 7x.
Divide both sides by 7: x = 2.
Substitute this value into either of the original equations to find y. y = -4(2) + 9 = 1.
So the solution to the system is x = 2 and y = 1.
Therefore, the correct answer is (2, 1).