How do you solve the system of equations #-2x + 4y = 10 # and #3x - 6y = - 15#?

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Answer 1 · 2018-06-20T09:06:49

#color(crimson)("As equations (1), (2) are the same, we cannot solve for x & y."#

#-2x + 4y = 10#

#-x + 2y = 5, " Eqn (1)"#

#3x - 6y = -15#

#x - 2y = -5, " Eqn (2)"#

As equations (1), (2) are the same, we cannot solve for x & y.

Answer 2 · 2018-06-20T10:21:36

The system has infinitely many solutions. See explanation.

The system is:

#{(-2x+4y=10),(3x-6y=-15):}#

We can divide the first equation by #-2# and second by #3# and the equations become the same:

This means that any pair #(x,y)# fulfilling the equation (1) is also the solution to the initial system.

Example solutions are then:

#(-5;0)#, #(0;2 1/2)#, #(5;5)#