Question is in description.

Question

Solve the following system of linear equations by graphing:
4x + 2y = −20

10x + 5y = −50

Select whether the system is consistent, inconsistent, or dependent. If the system is consistent, enter that point in the boxes below.

 

Answer 1

4x+2y =-20

solve for y

2y=-4x -20

y =-2x -10 is a line with slope =-2 and y intercept -10

10x +5y =-50

5y = -10x -50

y =-2x -10 is the same line with slope -2 and intercept -10

the equations are identical, graphically they are the same line. They "intersect" at every point on the line. There are an infinite number of solutions. The two equations are linearly dependent. Multiply the first equation by 2.5 and it is the 2nd equation

4x + 2y =-20

2.5(4x) + 2.5(2y) =2.5(-20)

10x + 5y = -50

any solution (x,y) to the 1st equation is also a solution to the 2nd equation

(0, -10), (1, -12), (2, -14), (3, -16), (4,-18) ... are all solutions to both equations