x+y=4 and x-y=2

Question

use graphical method to solve the given system of equations for x and y.

Answer 1

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

The first equation is x + y = 4    →(1)

Subtract x from each side.

y = - x + 4.

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

slope = - 1 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 = -1/1

Start at point (0, 4), move 1 unit down and 1 unit right, then plot the point (1, 3).

The second equation is x - y = 2  →(2)

Subtract x from each side.

- y = - x + 2

y = x - 2.

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

slope = 1 and y-intercept is - 2.

y-intercept is - 2, so the line crosses the y-axis at (0, - 2)

Using slope find the next point.

Slope = rise/run = 1/1

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

Draw two lines through these points.

Graph :

From the graph the intersection point is (3, 1).

So,the solution of the system ix x = 3 and y = 1.