Final answer:
To solve the system of equations x + 9y = 29 and 2x + 8y = 28, you can use either the substitution method or the elimination method. The solution to the system is x = 2 and y = 3.
Step-by-step explanation:
To solve the system of equations x + 9y = 29 and 2x + 8y = 28, you can use either the substitution method or the elimination method. Let's use the elimination method:
Multiply the first equation by 2 to make the coefficients of x in both equations equal. This gives us 2x + 18y = 58.
Subtract this new equation from the second equation, eliminating x: (2x + 8y) - (2x + 18y) = 28 - 58. Simplifying gives us -10y = -30, which can be further simplified to y = 3.
Now, substitute the value of y into one of the original equations. Let's use the first equation: x + 9(3) = 29. Simplifying gives us x + 27 = 29. Subtracting 27 from both sides gives us x = 2.
Therefore, the solution to the system of equations is x = 2 and y = 3.