Solve graphically the system of linear equations:

Question

x+y=0 −3x+4y=14

Answer 1

there are many fine online graphing sites.
desmos.com is a handy one.

Answer 2

Draw Cartesian coordinate system.

Find two points on line x + y = 0

For example:

x = 5

x + y = 0

5 + y = 0

subtract 5 to both sides

y = - 5

x = - 3

x + y = 0

- 3 + y = 0

Add 3 to both sides

y = 3

Mark points ( 5 , - 5 ) ( - 3 , 3 ) and draw straight line.

Find two points on line 3 x + 4 y = 14

x = 0

3 x + 4 y = 14

3 ∙ 0 + 4 y = 14

0 + 4 y = 14

4 y = 14

y = 14 / 4 = 2 ∙ 7 / 2 ∙ 2 = 7 / 2 = 3.5

y = 0

3 x + 4 y = 14

3 x + 4 ∙ 0 = 14

3 x + 0 = 14

3 x = 14

x = 14 / 3 = 4.66666

Mark points ( 0 , 3.5 ) ( 4.66666 , 0 ) and draw straight line.

The x and y coordinates of the intersection will be the solution to the system of equations.

The solution is x = - 2 , y = 2