2x+y=3 and -x+y=0

Question

solve the system by graghing.

Answer 1

The system of equations are 2x + y = 3 and - x + y = 0

The first line equation is 2x + y = 3

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

y = - 2x + 3

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

slope = - 2 and y - intercept is 3.

y - intercept is 3, so the line crosses the y - axis at origin (0, 3).

Using slope find the next point.

Slope = rise/run = - 2/1

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

Draw a line through these points.

The second line equation is - x + y  = 0.

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

y = x

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

slope = 1 and y - intercept is 0.

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

Using slope find the next point.

Slope = rise/run = 1/1

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

Draw a line through these points.

Graph :

From the graph lines are intersecting at (1, 1).

So, the solution of the given system is x = 1 and y =1.