To solve the system of equations:
1. Start by setting the two equations equal to each other:
y = 2x - 1
y = 5 - x
2. Since both equations are equal to y, we can set them equal to each other:
2x - 1 = 5 - x
3. Simplify the equation by combining like terms:
2x + x = 5 + 1
3x = 6
4. Divide both sides of the equation by 3 to solve for x:
x = 2
5. Substitute the value of x back into one of the original equations to solve for y. Let's use the first equation:
y = 2(2) - 1
y = 4 - 1
y = 3
Therefore, the solution to the system of equations is x = 2 and y = 3.
Now, let's graph the equation y = 5 - x:
To graph the equation, we can create a table of values by choosing different values for x and calculating the corresponding values of y. Here are some points that lie on the graph:
x | y
-----
0 | 5
1 | 4
2 | 3
3 | 2
4 | 1
Plot these points on a coordinate plane and connect them to form a straight line. The graph of y = 5 - x will have a negative slope of -1 and intersect the y-axis at 5.
I hope this helps! Let me know if you have any further questions.