Determine if the two lines are intersecting, parallel or the same lines by comparing the linear equations in slope - intercept form. State how many solutions there will be for each system.
Y = 4x - 5
8x + y = 3
To determine if the lines are intersecting, parallel, or the same, we can compare the slopes of the two equations.
The first equation is in slope-intercept form, y = mx + b, where m represents the slope. The slope of the first equation is 4.
The second equation is not in slope-intercept form, so we need to rearrange it. Subtracting 8x from both sides gives us y = -8x + 3. Comparing this form to the slope-intercept form, we see that the slope is -8.
Since the slopes are different (4 and -8), the lines are neither parallel nor the same. Therefore, they must be intersecting.
As for the number of solutions, intersecting lines have exactly one solution.