Question

the system of equations y =-3x+2 and y =1/2 x -6 is shown on the graph below. What is a reasonable estimate for the solution>

Answer 1

The reasonable estimate for the solution is (2.29, -4.87)

The reasonable estimate for the solution is the point where the two lines intersect each other.

To get the point where they intersect, we will simply equate the system of equations given as shown:

$-3x+2=\frac{1}{2}x-6\\Collect \ the \ like \ terms\\-3x-\frac{1}{2}x=-6-2\\\frac{-7x}{2}=-8\\-7x=-16\\x=\frac{16}{7} \\x=2.29$

Substitute x = 2.29 into any of the equation

Using the equation y = -3x+2

y = -3(2.29)+2

y = -6.87+2

y =-4.87

This shows that the reasonable estimate for the solution is (2.29, -4.87)

Further explanation about the system of equations can be found here https://brainly.com/question/19713330

Answer 2

The point of intersection of the linear equations is approximately $(x,y) = (2.286, -4.857)$.

The most quickest approach that offers a reasonable solution consist in representing both linear functions graphically by means of a graphing tool (i.e. Desmos). As there is a system of two equation and two variables, the system can be represented by 2D-graphing tool.

The solution of this system is represented by the point, in which both lines intercepts each other. Let be the following two linear functions:

$y = 3\cdot x + 2$ (1)

$y = \frac{1}{2}\cdot x - 6$ (2)

The result from graphic tool is presented below and the point of intersection is approximately $(x,y) = (2.286, -4.857)$.