how to graph the following equation.

Question

2x-y=4

x+2y=7

 

Please show me the steps in order to solve these two equations and the points I need in order to graph these equations.

 

Can you please show me the graph with the lines.

Answer 1

First, lets get these equations in slope-intercept form.

 

2x - y = 4  ------>  -y = -2x + 4  ----->   y = 2x - 4                  line 1

 

x + 2y = 7  ----->   2y = -x + 7  ----->  y = (-1/2)x + 7/2           line 2

 

 

We will graph these 2 lines on the same coordinate system. 

 

line 1:

 

Plot the y-intercept.  The y-intercept is the point when x=0.  The y-intercept is (0, -4).   Then we plot the next point using the slope and the first point.  The first point is (0, -4) and the slope is 2.  From this first point, we move 1 unit to the right, then 2 units up.  The point becomes (1, -2).

 

We have two points:  (0, -4) and (1, -2).  Connect these points throughout the entire coordinate system.

 

 

line 2:

 

The first point is the y-intercept.  The first point is (0, 3.5).  To plot the second point, we move 2 units to the right the first point, then move 1 unit down.  The second point is (2, 1.5).  

 

Connect these two points just like we did in line 1.

 

Okay, now we have constructed 2 lines on the same coordinate system.  Look for the point these two lines have in common.  This is the point of intersection and is your solution.