Final answer:
The solution to the system of equations y = -x + 9 and y = 3x + 8 is obtained by setting the two equations equal to each other, combining like terms, and solving for x first (x = 1/4) and then substituting that value into either original equation to find y (y = 35/4), resulting in the solution (1/4, 35/4).
Step-by-step explanation:
To solve the system of equations involving y = -x + 9 and y = 3x + 8, we can use the method of substitution or elimination. Both equations are structured to show y in terms of x, which means we can set them equal to each other since they both equal y:
-x + 9 = 3x + 8
Next, we combine like terms by adding x to both sides and subtracting 8 from both sides:
1 + 9 - 8 = 3x + x
Combining like terms, we get:
1 = 4x
Now, divide both sides by 4 to isolate x:
x = 1/4
Once we have x, we can substitute it back into either original equation to solve for y. Using y = -x + 9:
y = -(1/4) + 9
y = 9 - 1/4
y = 8.75 or y = 35/4
Therefore, the solution to the system of equations is (1/4, 35/4).