Question

question
type the correct answer in the box.
based on the graph produced in part a, what is the solution to this system of equations?
y = 5x - 5
y = (1/2)x + 5
write your answer as an ordered pair, (x,y).
the solution to this system of equations is .

Explanation:

Step1: Set equations equal

Since \( y = 3x - 5 \) and \( y=\frac{1}{2}x + 5 \), set \( 3x - 5=\frac{1}{2}x + 5 \).

Step2: Solve for x

Subtract \( \frac{1}{2}x \) from both sides: \( 3x-\frac{1}{2}x - 5=5 \).
Simplify: \( \frac{5}{2}x - 5 = 5 \).
Add 5 to both sides: \( \frac{5}{2}x=10 \).
Multiply by \( \frac{2}{5} \): \( x = 10\times\frac{2}{5}=4 \).

Step3: Find y

Substitute \( x = 4 \) into \( y = 3x - 5 \): \( y = 3(4)-5=12 - 5 = 7 \).

Answer:

\((4, 7)\)