How do I use elimination to find the solution of the system of equations #y=1/3x+7/3# and #y=−5/4x+11/4#?

1 Answer
Jul 9, 2015

Answer:

You multiply each equation by the LCM of the denominators and then solve by elimination as usual.

Explanation:

(1) #y = 1/3x+7/3#
(2) #y = -5/4x + 11/4#

Step 1: Multiply each equation by the least common multiple (LCM) of the denominator.

Multiply Equation 1 by #3# and Equation 2 by #4#.

(3) #3y = x+7#
(4) #4y = -5x + 11#

Step 2: To solve by elimination, multiply Equation 3 by #5#.

(5) #15y = 5x+35#
(4) #4y = -5x + 11#

Step 3: Add the two equations.

#19y = 46#

(6) #y= 46/19#

Step 4: Substitute Equation 6 into Equation 3.

#x+7 = 3y = 3×46/19 = 138/19#

#x= 138/19 -7 = (138-133)/19 = 5/19#

The solution is #x = 5/19#, #y = 46/19#

Check:

Substitute in Equation 1.

#y = 1/3x+7/3#

#46/19 = 1/3× 5/19 + 7/3 = 5/57 + 7/3 = 5/57 + 133/57 =138/57 =46/19#

Substitute in Equation 2.

#y = -5/4x + 11/4#

#46/19 = -5/4× 5/19 + 11/4 = -25/76 + 11/4 = -25/76 + 209/76 = 184/76 = 46/19#