Question #0fad0

1 Answer
Apr 10, 2017

Answer:

a) #(2/3, 10/3)#

b) #a = -36/11 = -3 3/11, b = 5/11#

Explanation:

a) For the first system of equations use elimination because you have a #+y# in the first equation and a #-y# in the second equation. Add the two equations directly:

#" "x + y = 4#
#"+ "2x - y = -2#

#" " 3x = 2; " "x = 2/3#

Substitute #x# back into one of the equations to find #y#:
#2/3 + y = 4/1*3/3#
#y = 12/3 - 2/3 = 10/3#

Solution a) #(2/3, 10/3)#

To check to see if this is correct, put this point into the second equation:
#2/1*2/3 - 10/3 = -6/3 = -2#

b) Rearrange the first equation to get #b = 2a + 7#
Substitute this equation into the second equation:
#-5a -3(2a + 7) = 15#

Distribute: #-5a -6a -21 = 15#

Add like-terms: #-11a -21 +21 = 15 + 21#

Simplify: #-11a = 36#

Divide by #-11: a = -36/11 = -3 3/11#

Substitute this value into #b = 2a + 7# to find #b#:
#b = 2*-36/11 + 7/1 * 11/11#
#b = -72/11 + 77/11 = 5/11#

Check the answer by inputting it into the second equation:
#-5/1*-36/11 - 3/1*5/11 = 180/11 - 15/11 = 165/11 = 15#