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

Answer 1

See a solution process below:

To solve this by graphing, plot two points for each equation, draw a line through the two points, and note the intersection of the lines for each equation.

Formula 1:

Plot the two points after solving the equation for them, then draw a line through them:

#y = (4 * 0) - 3#
#y = 0 - 3#
#y = -3# or #(0, -3)#
#y = (4 * 1) - 3#
#y = 4 - 3#
#y = 1# or #(1, 1)#

graph{(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]

Find the intersection of the lines:

graph{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)#

The system of equations is regarded as consistent because it shares at least one point.

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Answer 2

To solve the system of equations y = 4x - 3 and y = 1 by graphing, you would plot both lines on the coordinate plane. The first line y = 4x - 3 has a slope of 4 and a y-intercept of -3. The second line y = 1 is a horizontal line passing through the y-coordinate 1. The point of intersection between these two lines represents the solution to the system. The system is classified as consistent and independent since it has exactly one solution.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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