Asked by Yur
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.
Answers
Answered by
GPT 3.5
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 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.