How do i determine the point of intersection of the linear functions 2x − y = 4 and x + 2y + 3 = 0?

2 Answers
sjc
May 20, 2017

#(1,-2)#

Explanation:

Solve them simultaneously; in this case elimination seems the better option.

#2x-y=4---(1)#

#x+2y=-3--(2)#

multiply #(1)# by #" "2" "# to get the coefficients of #y# the same.

#4x-2y=8--(1a)#

#x+2y=-3--(2)#

#(1a)+(2)#

#5x=5#

#=>x=1#

substitute into#" " (2)#

#1+2y=-3#

#2y=-4#

#=>y=-2#

check in #(1)

LHS

#2xx1- -2=2+2=4#

#=#RHS

intersection points#" "(1,-2)#

Jim G.
May 20, 2017

#(1,-2)#

Explanation:

#2x-color(red)(y)=4to(1)#

#x+2color(red)(y)+3=0to(2)#

#"from " (1) " we can express y in terms of x"#

#rArrcolor(red)(y)=2x-4to(3)#

#" substitute this value of y into " (2)#

#rArrx+2(2x-4)+3=0#

#rArrx+4x-8+3=0larr" distributing"#

#rArr5x-5=0larr" simplifying"#

#"add 5 to both sides"#

#5xcancel(-5)cancel(+5)=0+5#

#rArr5x=5rArrx=1#

#"substitute this value into " (3)" and evauate for y"#

#y=2-4=-2#

#color(blue)"As a check"#

Substitute these values into ( 2) and if equation is true the these are the solution.

#1+(2xx-2)+3=0rarr" True"#

#rArr"point of intersection "=(1,-2)#
graph{(y-2x+4)(y+1/2x+3/2)=0 [-10, 10, -5, 5]}

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