solve the system of equation by graphing. 2x-y=-6, x+2y=2

Question

solve the system of equations by graphing.

2x-y=-6

x+2y=2

Answer 1

Given equations are 2x-y = -6

Subtrct 2x from each side.

2x-2x-y = -2x-6

Multiple to each side by negitive one.

y = 2x+6

And x+2y = 2

Subtract x from each side.

x-x+2y = -x+2

Multiple to each side by 2.

2y/2 = -1/2x+2/2

y = -1/2x+1

To find coordinate points substitute x = 0,1,-1 in above equations.

Then the points of first equation would be (0,6),(1,8),(-1,4)

Points of second equation would be (0,1),(1,1/2),(-1,3/2).

Graph of above equations

Draw the coordinate plane.

Plot the points.

Connect the plotted points.

Then the formed lines indicating given lines.

Observe the graph the two lines are iintersecting at (-2,2).

Solution of given system is x = -2,y = 2.

 

Answer 2

The system of equations are 2x - y = - 6 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 = - 6.

- y = - 2x - 6

y = 2x + 6.

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

slope = 2 and y - intercept is 6.

y - intercept is 6, so the line crosses the y - axis at (0, 6).

Using slope find the next point.

Slope = rise/run = 2/1

Start at point (0, 6), move 2 units up and 1 unit right, then plot the point (1, 8).

The second linear 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 linear system (x, y ) = (- 2, 2).