How do solve the following linear system?: # 5x+2y=1 , 5x-4y=23 #?

1 Answer

Answer:

See below

Explanation:

Basically, You use both equations to find the value of one variable and plug that into one of the equations given to get the value of the other variable.

#5x+2y=1, 5x-4y=23#

Solve equation 1 for #5x#:

#5x=1-2y#

Substitute into second equation:

#1-2y-4y=23#

Solve for #y#

#-6y=22 => color(blue)(y=-22/6=-11/3#

Then use the value of #y# and substitute it into one of the equations and solve for #x#:

#5x+2y=1#

#5x+2(-11/3)=1#

#5x-22/3=1#

#5x=25/3=>color(blue)(x=5/3#

Check by graphing (the circle shows the plotted point #(5/3,-11/3)#

graph{(5x+2y-1)(5x-4y-23)((x-5/3)^2+(y+11/3)^2-.1)=0}