solve the system of equations by graphing

Question

3x+5y=0
2x-5y=-25.

Answer 1

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

The first equation is 3x + 5y = 0.

Subtract 3x  from each side.

5y = - 3x

Divide each side by 5.

y = (- 3/5)x.

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

slope =- 3/5 and y-intercept is 0.

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

Using slope find the next point.

Slope = rise/run = - 3/5

Start at point (0, 0), move 3 units down and 5 units right, then plot the point (5, - 3).

The second equation is 2x - 5y = - 25.

Subtract 2x from each side.

 - 5y = - 25 - 2x.

Divide each side by negative 5..

 y = (2/5)x + 5.

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

slope = 2/5 and y-intercept is 5.

y-intercept is 5, so the line crosses the y-axis at (0, 5)

Using slope find the next point.

Slope = rise/run = 2/5

Start at point (0, 5), move 2 units up and 5 units right, then plot the point (5, 7).

Draw the lines through these points.

Graph :

Observe the graph, the solution of the system (x, y) = (- 5, 3).