Question

Solve the system of linear equations by graphing

{2x+y=6}

{4x+y=6}

What is the solution of the system of equation?

Answer 1

Given equations are 2x+y = 6

Subtract 2x from each side.

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

y = -2x+6 ---> (1)

And 4x+y = 6

Subtract 4x from each side.

4x-4x+y = -4x+6

y = -4x+6 ----> (2)

To find coordinate pairs substitute x = 0,1,-1 n equations (1)&(2).

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

Points of second equation is (0,6),(1,2),(-1,10)

Graph of above equations

Draw the coordinate plane.

Plot the above points.

Connect the ploted points.

Then the formed lines indicating given equations.

Observe the graph the two lines are intersecting at (0,6).

Solution of given system is x = 0, y = 6.

 

Answer 2

The system of linear equations are 2x + y = 6 and 4x + y = 6.

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

The first linear equation is 2x + y = 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 down and 1 unit right, then plot the point (1, 4).

The second linear equation is 4x + y = 6.

y = - 4x + 6.

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

slope = - 4 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 = - 4/1

Start at point (0, 6), move 4 units down and 1 unit right, then plot the point (1, 2).

Draw the lines through these points.

Graph :

Observe the graph, the solution of the linear system (x, y ) = (0, 6).