Use the graph method to solve the system of linear equations
Y equals negative X +3 and Y equals X minus one
(-1,2)
(0,3)
(1,0)
(1,2)
(2,1)
To solve the system of equations graphically, we need to plot both equations onto the same graph and see where they intersect.
The first equation is Y = -X + 3.
The second equation is Y = X - 1.
Let's plot both equations on the graph:
For Y = -X + 3:
- When X = 0, Y = 3
- When X = 1, Y = 2
- When X = 2, Y = 1
For Y = X - 1:
- When X = 0, Y = -1
- When X = 1, Y = 0
- When X = 2, Y = 1
Now, let's plot the points (-1,2), (0,3), (1,0), (1,2), and (2,1) on the graph.
The point of intersection is (1,2). Let's verify if this point satisfies the system of equations:
For Y = -X + 3:
When X = 1, Y = -1 + 3 = 2
For Y = X - 1:
When X = 1, Y = 1 - 1 = 0
Therefore, the solution to the system of equations is X = 1 and Y = 2.