X plus Y equals eight
Y equals negative X +3
Solve the system y equals negative X +3 and X plus Y equals eight by graphing shown that there is no solution to the system is the statement true false?explain.
To solve the system of equations graphically, we need to plot the two lines represented by the equations:
1) Y = -X + 3
2) X + Y = 8
First, let's rearrange equation 2 to solve for Y:
Y = 8 - X
Now we can plot both lines on a graph:
The line Y = -X + 3 has a y-intercept of 3 and a slope of -1.
The line Y = 8 - X has a y-intercept of 8 and a slope of -1.
When we graph both lines, we will see that they are parallel and will never intersect. This means there is no solution to the system of equations. This is because the two lines have the same slope (-1) but different y-intercepts (3 and 8), so they will never meet.
Therefore, the statement that there is no solution to the system is true.