How do you solve #5x - 1/2y = 24# and #3x - 2/3y = 41/3#?

1 Answer
Aug 23, 2015

Answer:

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

Explanation:

You can solve this system of equations by multiplication.

Start by rewriting your two equations so that you can work without denominators.

#{(10x - y = 48), (9x - 2y = 41):}#

Notice that you can multiply the first equation by #-2# so that you get

#10x - y = 48 | * (-2)#

#-20x + 2y = - 96#

You can now add the two equations to cancel the #y#-terms and solve for #x#. Add the left side of the equations and the right side of the equations separately to get

#-20x + color(red)(cancel(color(black)(2y))) + 9x - color(red)(cancel(color(black)(2y))) = -96 + 41#

#-11x = -55 implies x= ((-55))/((-11)) = color(green)(5)#

Use the value of #x# in either one of the two equations to find the value of #y#

#10 * 5 - y = 48#

#y = 50 - 48 = color(green)(2)#

The two solutions to this system of equations are

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