Identify any solutions to the system given below. 2x + y = 5 3y = 15 – 6x a(6, –7) b(2, 1) c(–2, –9) d(–4, 13)

The system of equations have many solutions and the correct options are A,B and D.

Explanation:

The given equations are,

    ..... (1)

 .... (2)

Simplify the second equation.

Divide both sides by 3.

It is same as equation (1). Since equation (1) and (2) are same, therefore all the points lies on the line or which satisfies the equation are the solution of the given system of equations.

Test the points whether the point lies on the line or not.

Check for point A(6,-7).

LHS and RHS are equal, therefore the point A is the solution of the system of equations.

Check for point B(2,1).

LHS and RHS are equal, therefore the point B is the solution of the system of equations.

Check for point C(-2,-9).

LHS and RHS are not equal, therefore the point C is not the solution of the system of equations.

Check for point D(-4,13).

LHS and RHS are equal, therefore the point D is the solution of the system of equations.

Therefore the options A,B and D are correct.

a

step-by-step explanation:

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.