How do you solve 5x+6y=24 and 3x+5y=18?
1 Answer
Explanation:
Your starting system of equations is
#{(5x + 6y = 24), (3x + 5y = 18):}#
Multiply the first equation by
#{(5x + 6y = 24| * (-3)), (3x + 5y = 18| * 5):}#
#{(-15x - 18y = -72), (15x + 25y = 90):}#
Notice that if you add these two equations, more specifically if you add the left-hand sides and the right-hand sides separately, you can eliminate the
This will allow you to solve the resulting equation for
#{(-15x - 18y = -72), (15x + 25y = 90):}#
#stackrel("-------------------------------------------------------")#
#color(red)(cancel(color(black)(15x))) - 18y + color(red)(cancel(color(black)(15x))) + 25y = -72 + 90#
#7y = 18 implies y = color(green)(18/7)#
Now use this value of
#5x + 6 * 18/7 = 24#
#35x + 108 = 168#
#35x = 60 implies x = color(green)(12/7)#