Consider the following system of equations.
{y=3x-5
y=−x+7
Are the graphs of the two lines intersecting lines, the same line, or parallel lines? Explain your reasoning.
How many solutions does the system have? Explain how you can tell without solving the system.
The graphs of the two lines are intersecting lines. This can be seen by comparing the slopes of the two lines, which are 3 and -1 respectively. Since the slopes are not equal, the lines must intersect.
The system has one solution. This can be seen by subtracting the two equations, which results in 4x = 12. Solving for x gives x = 3, and then substituting this value into either of the original equations gives y = 6. Therefore, the system has one solution, (3, 6).
ahhh, the bot did so well to get the correct x = 3, but then messed up
its answer of (3,6) does not satisfy either equation.
if x = 3, y = 3(3) - 5 = 4
So the solution is (3,4)