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 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.
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 false, because the lines have an intersection point.
The correct response is: The statement is false, because the lines have an intersection point.
When graphing the two equations, y=-x+3 and x+y=8, we can plot the points and draw the lines. The first equation, y=-x+3, is a straight line with a negative slope that intersects the y-axis at (0, 3). The second equation, x+y=8, can be rewritten as y=-x+8, which has a negative slope and intersects the y-axis at (0, 8).
By graphing, we can see that the two lines intersect at the point (2, 6). Therefore, there is a solution to the system of equations and the statement that there is no solution is false.
The statement is false, because the lines have an intersection point.
To solve the system of equations y = -x + 3 and x + y = 8, we can graph the equations and determine if they intersect at a point or if they are parallel.
Let's start by graphing the first equation, y = -x + 3. To do this, we can plot a few points that satisfy the equation and then connect the points to form a line. For example, when x = 0, y = -0 + 3 = 3. So we can plot the point (0, 3). Similarly, when x = 1, y = -1 + 3 = 2, so we can plot the point (1, 2). By connecting these points, we get a line.
Next, let's graph the second equation, x + y = 8. We can again plot a few points that satisfy the equation and connect them to form a line. For example, when x = 0, y = 8 - 0 = 8, so we can plot the point (0, 8). When x = 1, y = 8 - 1 = 7, so we can plot the point (1, 7). By connecting these points, we get another line.
Now, if we look at the graph of these two lines, we can see that they intersect at a point. This indicates that there is a solution to the system of equations. Therefore, the statement is false, and the correct response is "The statement is false because the lines have an intersection point."