Solving the system y=-x+3 and x+y=8 by graphing shows that there's no solution to the problem is this true or false
False. Solving the system by graphing actually shows that the two lines intersect at the point (2, 6), which is the solution to the system.
False. Solving the system y=-x+3 and x+y=8 by graphing shows that the two lines intersect at the point (2, 6). Thus, there is a solution to the problem.
To solve the system of equations y = -x + 3 and x + y = 8 by graphing, you need to plot the two lines represented by these equations on a coordinate plane.
First, let's solve the first equation, y = -x + 3, to find its slope and y-intercept. Comparing this equation to the standard slope-intercept form, y = mx + b, we see that the slope is -1 and the y-intercept is 3. Therefore, we can plot a point at (0, 3) and use the slope to find another point. Since the slope is -1, we move one unit to the right and one unit down to get to the point (1, 2). Joining these two points, we can draw a line.
Now, let's solve the second equation, x + y = 8, to find its slope and y-intercept (although it's easier to find the x-intercept in this case). Rearranging the equation, we get y = -x + 8, where the slope is -1 and the y-intercept is 8. We can plot a point at (0, 8) and use the slope to find another point. Moving one unit to the right and one unit down, we get to the point (1, 7). Joining these two points, we can draw a line.
By graphing the two lines, you will notice that they intersect at the point (2, 6). This point is the solution to the system of equations, and it indicates that there is indeed a solution to the problem. Therefore, the statement "there's no solution to the problem" is FALSE.