When solving the system of equations by graphing, what is the solution of 3x + 2y = 2 and 2x – y = 6?

Question

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Answer 1

Given equations are 3x+2y = 2

2x-y = 6

Write the equations in slope intercept form.

y = (-3/2)x+1

y = 2x-6

Graph

From the graph we can observe the intersection point of given lines is (2,-2)

Solution x = 2, y = -2

 

Answer 2

The system of equations are 3x + 2y = 2 and 2x - y = 6.

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

The first equation is 3x + 2y = 2.

2y = - 3x + 2

y = (- 3/2)x + 1.

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

slope = - 3/2 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 = - 3/2

Start at point (0, 1), move 3 units down and 2 units right, then plot the point (2, - 2).

The second 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, - 4).

Draw the lines through these points.

Graph :

Observe the graph, the solution of the system (x, y ) = (2, - 2).