Solving the system y = -x + 3 and x + y = 8 by graphing shows that there is no solution to the system. Is this statement true or false? Explain. (1 point)
A. The statement is false, because the lines have an intersection point.
B. The statement is true, because the lines are parallel.
C. The statement is false, because the lines are parallel.
D. The statement is true, because the lines have an intersection point
A. The statement is false, because the lines have an intersection point.
When we graph the two given equations, we can see that the lines intersect at the point (2,6). This means that there is a solution to the system of equations. So, option A is the correct answer.
The correct answer is C. The statement is false, because the lines are parallel.
By graphing the two equations, we can see that they are both straight lines. The equation y = -x + 3 has a y-intercept of 3 and a slope of -1. The equation x + y = 8 can be rearranged to y = -x + 8. This equation also has a y-intercept of 8 and a slope of -1.
When two lines have the same slope but different y-intercepts, they are parallel and will never intersect. In this case, since both lines have a slope of -1, they are parallel. Therefore, there is no solution to the system of equations.
Therefore, the statement that there is no solution to the system is true because the lines are parallel.
To determine the validity of the statement, we need to graph the two equations and see if they intersect or are parallel.
The first equation is y = -x + 3. This is a linear equation in slope-intercept form, where the coefficient of x is -1, and the y-intercept is 3. This means that the line will have a negative slope and pass through the point (0, 3).
The second equation is x + y = 8. To put it in slope-intercept form, we can solve for y: y = -x + 8. Here, the coefficient of x is -1, and the y-intercept is 8. This line also has a negative slope and passes through the point (0, 8).
Let's plot these lines on a graph: