Respuesta :
Put both of those equations into slope intercept form (in order to be typed into the graphing calculator).
2x + 3y = 16.9
3y = -2x + 16.9
y = (-2/3)x + 16.9/3
5x = y + 7.4
5x - 7.4 = y
So in the graphing calculator,
Y1 = (-2/3)x + 16.9/3
Y2 = 5x - 7.4
Then find the point of intersection and the x value of that would be the solution.
You get the coordinate (2.3, 4.1). So x = 2.3, y = 4.1
2x + 3y = 16.9
3y = -2x + 16.9
y = (-2/3)x + 16.9/3
5x = y + 7.4
5x - 7.4 = y
So in the graphing calculator,
Y1 = (-2/3)x + 16.9/3
Y2 = 5x - 7.4
Then find the point of intersection and the x value of that would be the solution.
You get the coordinate (2.3, 4.1). So x = 2.3, y = 4.1
Taking into account the definition of a system of linear equations, the solution to the system of linear equations is x=2.3 and y=4.1
System of linear equations
A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.
Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is to say, the values of the unknowns must be sought, with which when replacing, they must give the solution proposed in both equations.
This case
In this case, the system of equations to be solved is
[tex]\left \{ {{2x+3y=16.9} \atop {5x=y+7.4}} \right.[/tex]
There are several methods to solve a system of equations, and it is decided to solve it using the graphical method, which consists of representing the equations on a graph, in the same coordinate system. The intersection of the lines representing the equations is the solution of the system.
In this case, the graph is observed in the attached figure, where it can be seen that the intersection of both lines is the point (x,y)= (2.3,4.1).
Finally, the solution to the system of linear equations is x=2.3 and y=4.1
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