Question

How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent `2x - 3y = 14` and `2x + y = -10`?

Answer 1

See a solution process below:

Explanation:

To graph the lines first find two points on the line. Then plot the points. Then draw a line through the points:

Equation 1:

For `x = 1`

`(2 * 1) - 3y = 14`

`2 - 3y = 14`

`-3y = 12`

`y = -4` or `(1, -4)`

For `x = 4`

`(2 * 4) - 3y = 14`

`8 - 3y = 14`

`-3y = 6`

`y = -2` or `(1, -2)`

graph{((x-1)^2+(y+4)^2-0.25)((x-4)^2+(y+2)^2-0.25)(2x-3y-14)=0 [-30, 30, -15, 15]}

Equation 2:

For `x = 0`

`(2 * 0) + y = -10`

`0 + y = -10`

`y = -10` or `(0, -10)`

For `x = -5`

`(2 * -5) + y = -10`

`-10 + y = -10`

`y = 0` or `(-5, 0)`

graph{(2x+y+10)(x^2+(y+10)^2-0.25)((x+5)^2+y^2-0.25)(2x-3y-14)=0 [-30, 30, -15, 15]}

We can see the the lines cross at `(-2, -6)` Because there is on solution the system is consistent.

graph{((x+2)^2+(y+6)^2-0.05)(2x+y+10)(2x-3y-14)=0 [-16, 16, -8, 8]}