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)
Responses
The statement is true, because the lines have an intersection point.
The statement is true, because the lines have an intersection point.
The statement is true, because the lines are parallel.
The statement is true, because the lines are parallel.
The statement is false, because the lines are parallel.
The statement is false, because the lines are parallel.
The statement is false, because the lines have an intersection point.
The statement is false, because the lines have an intersection point.
By graphing the two equations, we can see that the lines intersect at the point (2, 6). Therefore, there is a solution to the system.
The statement is false, because the lines have an intersection point.
To solve the system by graphing, we can plot the two lines on a coordinate plane.
The first equation, y = -x + 3, represents a line with a slope of -1 and a y-intercept of 3.
The second equation, x + y = 8, can be rearranged to y = -x + 8, which represents a line with a slope of -1 and a y-intercept of 8.
When we graph these lines, we will see that they intersect at the point (2, 6).
Therefore, there is a solution to the system, and the statement "there is no solution to the system" is false.
The statement is true, because the lines have an intersection point.
To explain why, let's first look at the system of equations:
1) y = -x + 3
2) x + y = 8
We can solve this system by graphing. To graph the equations, we can start by rewriting them in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
For equation 1, we can rewrite it as y = -1x + 3. The slope is -1 and the y-intercept is 3.
For equation 2, we can rewrite it as y = -1x + 8. Again, the slope is -1 and the y-intercept is 8.
Now we can graph the equations by plotting the y-intercepts and using the slope to find additional points on the lines.
For equation 1, we can start at the y-intercept (0, 3) and from there, we can move 1 unit to the right and 1 unit down to find another point, giving us the coordinates (1, 2). We can repeat this process to find more points if needed.
For equation 2, we can start at the y-intercept (0, 8) and from there, we can move 1 unit to the right and 1 unit down to find another point, giving us the coordinates (1, 7). Again, we can repeat this process to find additional points.
After plotting the points for both equations, we can draw the lines on the graph.
Now, if we observe the graph, we can see that the lines intersect at the point (2, 1). Therefore, there is a solution to the system of equations, contrary to the given statement.
Hence, the statement is false, because the lines do have an intersection point.