How do you solve 5x + y = 9 and 10x - 7y =-18?

1 Answer
Sep 8, 2015

Answer:

#{(x=1), (y=4) :}#

Explanation:

Take a look at your starting system of equations

#{(5x + y = 9), (10x - 7y = -18) :}#

Notice that if you multiply the first equation by #(-2)#, and add the right-hand sides and the left-hand sides of the equations separately, you can eliminate the #x#-term.

This will leave you with one equation with one unknown, #y#.

#{(5x + y = 9 | * (-2)), (10x - 7y = -18) :}#

#{(-10x -2y = -18), (10x - 7y = -18) :}#
#stackrel("---------------------------------------------------")#

#-color(red)(cancel(color(black)(10x))) - 2y + color(red)(cancel(color(black)(10x))) - 7y = -18 + (-18)#

#-9y = -36 implies y = ((-36))/((-9)) = color(green)(4)#

Now use this value of #y# in one of the two original equations to find the value of #x#

#5x + (4) = 9#

#5x = 5 implies x = 5/5 = color(green)(1)#