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

Jul 23, 2018

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 $x = 0$

$y = \left(4 \cdot 0\right) - 3$

$y = 0 - 3$

$y = - 3$ or $\left(0 , - 3\right)$

• For $x = 1$

$y = \left(4 \cdot 1\right) - 3$

$y = 4 - 3$

$y = 1$ or $\left(1 , 1\right)$

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 $\left(- 2 , 1\right)$

• For $x = 2$; $y = 1$ or $\left(2 , 1\right)$

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 $\left(1 , 1\right)$

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