Question

#8 solve the system. y = 2x - 2 y = 2x + 9 solution: the solution is (2,22) the solution is (-2,5) there is no solution. there are infinitely many solutions.

Explanation:

Step1: Analyze the slopes

The two equations are \( y = 2x - 2 \) and \( y = 2x + 9 \). In slope - intercept form \( y=mx + b \), the slope \( m \) of both lines is 2.

Step2: Analyze the y - intercepts

The y - intercept \( b \) of the first line \( y = 2x-2 \) is - 2, and the y - intercept of the second line \( y = 2x + 9 \) is 9. Since the slopes are equal and the y - intercepts are different, the two lines are parallel.

Step3: Determine the number of solutions

Parallel lines do not intersect, so there is no solution to the system of equations.

Answer:

There is no solution.