How do you solve -10x + y = 0 and 5x + 3y = -7?

1 Answer
Sep 6, 2015

Answer:

#{(x = -1/5), (y = -2):}#

Explanation:

Your starting system of equations looks like this

#{(-10x + y = 0), (5x + 3y = -7):}#

Multiply the second equation by #2# to get

#{(-10x + y = 0), (10x + 6y = -14):}#

If you add these equations by adding the left-hand side and the right-hand side separately, you can eliminate the #x#-term.

The resulting equation will only have one unknown, #y#.

#{(-10x + y = 0), (10x + 6y = -14):}#
#stackrel("-------------------------------------------")#
#-color(red)(cancel(color(black)(10x))) + y + color(red)(cancel(color(black)(10x))) + 6y = 0 + (-14)#

#7y = -14 implies y = (-14)/7 = color(green)(-2)#

Pick one of the original equations and substitute #y# with the value you've just calculated to get the value of #x#

#-10x + (-2) = 0#

#-10x = 2 implies x = color(green)(-1/5)#