Graph the system of equations to determine whether it has no solution, infinitely many solutions, or one solution:

Question

2x-y=4
x+2y=2

Answer 1

The given equations are  2x - y = 4    -> (1)

                                   x+2y  = 2    -> (2)

The equation (1) is multiply by 2

4x - 2y = 8

x +2y  = 2

___________

5x = 10

Therefore x = 2

Substitute the x value in equation  (2)

2+ 2y = 2

Therefore y = 0

The solution is (x, y) = (2, 0)

The system of the equations has one solution

Graph  the system of the equations

 

Answer 2

The system of equations are 2x - y = 4 and x + 2y = 2.

Write the equations in slope - intercept form : y = mx + b, where m is slope and b is y - intercept.

The first equation is 2x - y = 4.

- y = - 2x + 4

y = 2x - 4.

Compare the equation with slope - intercept form : y = mx + b.

slope = 2 and y - intercept is - 4.

y - intercept is - 4, so the line crosses the y - axis at (0, - 4).

Using slope find the next point.

Slope = rise/run = 2/1

Start at point (0, - 4), move 2 units up and 1 unit right, then plot the point (1, - 2).

The second equation is x + 2y = 2.

2y = - x + 2.

y = (-1/2)x + 1.

Compare the equation with slope - intercept form : y = mx + b.

slope = -1/2 and y - intercept is 1.

y - intercept is 1, so the line crosses the y - axis at (0, 1)

Using slope find the next point.

Slope = rise/run = - 1/2

Start at point (0, 1), move 1 unit down and 2 units right, then plot the point (2, 0).

Draw the lines through these points.

Graph :

Observe the graph,

The solution of the system (x, y ) = (2, 0).

The system of equations has one solution.