Question

How do you solve `y = 4x - 3`, `y = 1` by graphing and classify the system?

Answer 1

See a solution process below:

Explanation:

Two solve this by graphing, for each equation:
- Plot two points for each equation
- Draw a line through the two points
- Identify where the lines cross

Equation 1:

Solve the equation for two points and plot the two points then draw a line through the two points:

• For `x = 0`

`y = (4 * 0) - 3`

`y = 0 - 3`

`y = -3` or `(0, -3)`

• For `x = 1`

`y = (4 * 1) - 3`

`y = 4 - 3`

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

graph{(y-4x+3)(x^2+(y+3)^2-0.04)((x-1)^2+(y-1)^2-0.04)=0 [-10, 10, -5, 5]

Equation 2:

`y = 1` is a horizontal line where for each and every value of `x`, `y` is equal to `1`

• For `x = -2`; `y = 1` or `(-2, 1)`

• For `x = 2`; `y = 1` or `(2, 1)`

graph{(y-1)(y-4x+3)((x+2)^2+(y-1)^2-0.04)((x-2)^2+(y-1)^2-0.04)=0 [-10, 10, -5, 5]

Identify where the lines cross:

graph{(y-1)(y-4x+3)((x-1)^2+(y-1)^2-0.04)=0 [-10, 10, -5, 5]

We can see from the graphs the lines cross at `(1, 1)`

Because there is at least one point in common the system of equations is considered to be Consistent