# How do you solve # 2x – y = 4#, #3x + y = 1# by graphing and classify the system?

See a solution process below:

We can locate two points on the line for each equation, graph the line by drawing a line through the points.

Formula 1

graph{[-15, 15, -7.5, 7.5]}(x^2+(y+4)^2-0.05)((x-2)^2+y^2-0.05)(2x-y-4)=0

Formula 2

graph{(3x+y-1)(x^2+(y-1)^2-0.05)((x-2)^2+(y+5)^2-0.05)(2x-y-4)=0 [-15, 15, -7.5, 7.5]}

Solution

Consequently:

The system is independent because the slopes of the lines differ, and it is consistent because there is at least one solution.

graph{(3x+y-1)(-2x-y-4)=0 [-6, 6, -3, 3]}((x-1)^2+(y+2)^2-0.015)

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To solve the system of equations (2x - y = 4) and (3x + y = 1) by graphing, first rearrange each equation to solve for (y) in terms of (x). Then, plot the two lines on the same coordinate plane and identify the point where they intersect. This point represents the solution to the system. Finally, classify the system based on the number of solutions it has.

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To solve the system of equations ( 2x - y = 4 ) and ( 3x + y = 1 ) by graphing, follow these steps:

- Rewrite each equation in slope-intercept form ( y = mx + b ) to graph them easily.

For the first equation ( 2x - y = 4 ): [ -y = -2x + 4 ] [ y = 2x - 4 ]

For the second equation ( 3x + y = 1 ): [ y = -3x + 1 ]

- Plot the graphs of the two equations on the same coordinate plane.

The graph of ( y = 2x - 4 ) is a line with a slope of 2 and y-intercept of -4. The graph of ( y = -3x + 1 ) is a line with a slope of -3 and y-intercept of 1.

- Determine the point of intersection of the two lines.

The point of intersection represents the solution to the system of equations. In this case, the point of intersection is where the two lines intersect on the graph.

- Classify the system based on the number of solutions.

If the lines intersect at a single point, the system has one unique solution, which means the equations are consistent and independent. If the lines are parallel and do not intersect, the system has no solution, indicating inconsistent equations. If the lines coincide (overlap), the system has infinitely many solutions, indicating dependent equations.

After graphing the equations and finding the point of intersection, you can determine the classification of the system based on the number of solutions.

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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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