How do you solve the system of equations #9x + y = 8# and #- 7x - 2y = 6#?

3 Answers
Jan 27, 2018

#x=2#
#y=-10#

Explanation:

#9x+y=8# ...(1)
#-7x-2y=6# ...(2)

multiply for 2 the equation (1)

#(2)(9x+y=8)#
#-7x-2y=6#

#18x+2y=16#
#-7x-2y=6#

now adding both equations

#18x-7x+2y-2y=16+6#

#11x=22#
#x=2#

for y just replace in any equation

in (1)

#9(2)+y=8#
#18+y=8#
#y=8-18#

#y=-10#

Jan 27, 2018

#(x,y)to(2,-10)#

Explanation:

#9x+y=8to(1)#

#-7x-2y=6to(2)#

#"from equation "(1)#

#y=8-9xto(3)#

#"substitute "y=8-9x" in equation "(2)#

#-7x-2(8-9x)=6#

#rArr-7x-16+18x=6#

#rArr11x-16=6#

#"add 16 to both sides"#

#rArr11x=22#

#"divide both sides by 11"#

#rArrx=2#

#"substitute "x=2" in equation "(3)#

#rArry=8-18=-10#

#"point of intersection "=(2,-10)#

Jan 27, 2018

See a solution process below:

Explanation:

Step 1) Solve the first equation for #y#:

#9x + y = 8#

#9x - color(red)(9x) + y = 8 - color(red)(9x)#

#0 + y = 8 - 9x#

#y = 8 - 9x#

Step 2) Substitute #(8 - 9x)# for #y# in the second equation and solve for #x#:

#-7x - 2y = 6# becomes:

#-7x - 2(8 - 9x) = 6#

#-7x - (2 xx 8) + (2 xx 9x) = 6#

#-7x - 16 + 18x = 6#

#-7x + 18x - 16 = 6#

#(-7 + 18)x - 16 = 6#

#11x - 16 = 6#

#11x - 16 + color(red)(16) = 6 + color(red)(16)#

#11x - 0 = 22#

#11x = 22#

#(11x)/color(red)(11) = 22/color(red)(11)#

#(color(red)(cancel(color(black)(11)))x)/cancel(color(red)(11)) = 2#

#x = 2#

Step 3) Substitute #2# for #x# in the solution to the first equation at the end of Step 1 and calculate #y#:

#y = 8 - 9x# becomes:

#y = 8 - (9 xx 2)#

#y = 8 - 18#

#y = -10#

The Solution Is:

#x = 2# and #y = -10#

Or

#(2, -10)#