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. %0D%0A%0D%0A(1 point)%0D%0AResponses%0D%0A%0D%0AThe statement is true, because the lines are parallel.%0D%0AThe statement is true, because the lines are parallel.%0D%0A%0D%0AThe statement is false, because the lines have an intersection point.%0D%0AThe statement is false, because the lines have an intersection point.%0D%0A%0D%0AThe statement is true, because the lines have an intersection point.%0D%0AThe statement is true, because the lines have an intersection point.%0D%0A%0D%0AThe statement is false, because the lines are parallel.
The correct answer is:
The statement is false, because the lines have an intersection point.
To solve the system by graphing, we can plot the two given equations on a coordinate plane and see where the lines intersect.
The first equation, y = -x + 3, has a slope of -1 and a y-intercept of 3. This means that if we start at the point (0, 3), we can move down 1 unit and right 1 unit to find another point on the line. Similarly, if we start at (0, 3), we can move up 1 unit and left 1 unit to find another point.
The second equation, x + y = 8, can be rewritten as y = -x + 8. This equation also has a slope of -1, but a y-intercept of 8. So, if we start at the point (0, 8), we can move down 1 unit and right 1 unit to find another point on the line. Also, if we start at (0, 8), we can move up 1 unit and left 1 unit to find another point.
Graphing the two lines, we can see that they intersect at the point (2, 6). Therefore, there is a solution to the system, and the statement is false.
The statement is false, because the lines have an intersection point.
To solve the system, we can graph the two equations on a coordinate plane. The first equation, y = -x + 3, represents a line with a negative slope (m = -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 negative slope (m = -1) and a y-intercept of 8.
Plotting these lines on a graph, we can see that they intersect at the point (2, 6). Therefore, there is a solution to the system, and the statement that there is no solution to the system is false.
The correct response is:
The statement is false, because the lines have an intersection point.
Explanation:
To solve the system of equations y = -x + 3 and x + y = 8 by graphing, we need to graph both equations on a coordinate plane and see if the lines intersect at any point.
First, let's graph the equation y = -x + 3. We can start by plotting a few points on the graph. For example, when x = 0, y = 3. When x = 1, y = 2. When x = 2, y = 1. We can continue plotting other points, or we can use the slope-intercept form of the equation to find the slope and y-intercept.
The equation y = -x + 3 is in slope-intercept form, y = mx + b, where m represents the slope and b represents the y-intercept. In this case, the slope is -1, meaning that for every increase of 1 in the x-coordinate, the y-coordinate decreases by 1. The y-intercept is 3, so the line crosses the y-axis at (0, 3). By connecting the points or using the slope-intercept form, we can draw a line representing this equation on the graph.
Next, let's graph the equation x + y = 8. To do this, we can rearrange the equation to y = -x + 8. Again, we can plot points or use the slope-intercept form. The slope is -1, and the y-intercept is 8, so the line crosses the y-axis at (0, 8).
Now that we have both lines graphed on the same coordinate plane, we can visually see if they intersect. If the lines intersect at a point, it means there is a solution to the system of equations. In this case, when we draw the lines on the graph, we can see that they intersect at the point (2, 6). Therefore, there is a solution to the system of equations.
Therefore, the correct response is: The statement is false because the lines have an intersection point.