How do you solve this system of equations: #3x - y = 4 , 5x + 2y - 10= 0#?

1 Answer
Jim G.
Sep 20, 2017

#(x,y)to(18/11,10/11)#

Explanation:

#3x-y=4to(1)#

#5x+2y-10=0to(2)#

#"rearrange "(1)" in terms of x"#

#rArry=3x-4to(3)#

#"substitute "y=3x-4" into "(2)#

#5x+2(3x-4)-10=0#

#rArr5x+6x-8-10=0#

#rArr11x-18=0#

#"add 18 to both sides of the equation"#

#11xcancel(-18)cancel(+18)=0+18#

#rArr11x=18#

#"divide both sides by 11"#

#(cancel(11) x)/cancel(11)=18/11#

#rArrx=18/11#

#"substitute this value into "(3)#

#y=(3xx18/11)-4=54/11-44/11=10/11#

#rArr"point of intersection "=(18/11,10/11)#
graph{(y-3x+4)(y+5/2x-5)=0 [-16.02, 16.02, -8.01, 8.01]}

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