How do you solve this set of linear equations: #36x + 19y = 35; 10x + 12y = 19#?

1 Answer
Jun 3, 2017

Answer:

#x=59/242# and #y=167/121#

Explanation:

Strategy: There are several different options to solving these equations. This one may be susceptible to picking one of them and solving for #x# in terms of #y#. Then plug that equation with #y#s into the other equation. Then solve for #y#. Finally, with #y# equal to some value, plug it in to the first equation and solve for #x#.

Step 1. Pick one equation and solve for #x#.

Pick one of the two equations. It doesn't matter which.
#36x+19y=35#

Subtract #19y# from both sides.
#36x=-19y+35#

Divide both sides by #36#.
#color(red)(x=-19/36 y +35/36)#

Step 2. Plug that equation into the other, #10x+12y=19#.

#10color(red)(x)+12y=19#

#10(color(red)(-19/36 y +35/36))+12y=19#

Step 3. Solve for #y#.

Multiply #10# through.
#-190/36y+350/36+12y=19#

Subtract #350//36# from both sides.
#-190/36y+12y=19-350/36#

#121/18y=167/18#

Multiply both sides by #18//121#.
#y=167/18xx18/121#

#color(blue)(y=167/121)#

Step 3. Plug this into your #x# equation of Step 1.

#x=-19/36 color(blue)(y) +35/36#

#x=-19/36 (color(blue)(167/121)) +35/36#

#x=-19/36 (color(blue)(167/121)) +35/36#

#x=59/242#

ANSWER: #x=59/242# and #y=167/121#