Question

Решите с помощью графиков систему уравнений у = х - 1 у = -х +3

Answer 1

Графиками данных функций являются прямые, которые можно построить по двум точкам, например:
у=х-1, (1;0), (4;3) - зеленый график, 
у=-х+3 (1;2), (3;0) - красный график.
Решением является значение х точки пересечения этих графиков х=2.
Ответ: 2.

Answer 2

Solving the System of Equations

To solve the system of equations \( u = x - 1 \) and \( y = -x + 3 \) using graphs, we can plot the two equations on the same graph and find the point of intersection. The coordinates of the point of intersection will give us the solution to the system of equations.

Let's proceed with plotting the graphs of the given equations.

Graphical Representation

The graph of the equation \( u = x - 1 \) is a straight line with a slope of 1 and a y-intercept of -1. The graph of the equation \( y = -x + 3 \) is also a straight line with a slope of -1 and a y-intercept of 3.

By plotting these two lines on the same graph, we can find the point of intersection, which will give us the solution to the system of equations.

Solution

The solution to the system of equations \( u = x - 1 \) and \( y = -x + 3 \) is the point of intersection of the two graphs. By visually inspecting the graph, we can see that the point of intersection occurs at the coordinates (2, 1).

Therefore, the solution to the system of equations is: - \( u = 2 - 1 = 1 \) - \( y = -2 + 3 = 1 \)

So, the solution to the system of equations is (1, 1).

I hope this helps! If you have any further questions, feel free to ask.