#color(brown)("You have 2 unknowns and 2 equations so it is solvable.")#

#color(brown)("Two ways of solving:")#

## #color(blue)("Method 1")#

In detail: every step shown!!

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Consider #-5x-2y=3 # making #y# the dependant variable

#color(brown)("Showing the method for changing the variable for "5x-2y=3" only.")#

Add #color(green)(2y)# to both sides giving:

# (-5x-2y) color(green)(+2y) = (3)color(green)(+2y)#

#-5x = 3 +2y#

Subtract #color(green)(3)# from both sides giving:

#(-5x) color(green)(-3) =(2y+3)color(green)(-3)#

#-5x-3=2y#

Divide both sides by #color(green)(2)#

Note that divide by 2 is the same as multiply by #1/2#

#color(green)(1/2) (-5x-3) =color(green)(1/2)(2y)#

#-5/2x -3/2 = y#

Write as #color(blue)(y=-5/2x-3/2 ....................................(1))#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#color(brown)("Changing the variable for "2x-y =-6)#

#color(blue)(y=2x+6........................................................(2))#

Subtract #color(green)((1))# from (2) giving:

#y - color(green)(y)=2x -color(green)((-5/2x)) +6 -color(green)((-3/2))#

#0=9/2 x + 15/2#

#9/2x = -15/2#

Multiply throughout by 2 giving:

#9x=15#

#color(blue)(x=15/9................................................(3))#

Next step I will leave for you to do!

Substitute (3) into either of (1) or (2) to find the value of y

## #color(blue)("Method 2")#

#-5/2x-3/2 =y =2x+6#

#-5/2x-3/2 =2x+6#

Now solve for x and substitute in (1) or (2) to find y

#color(red)("Both methods are fast once you are")#

#color(red)("able to "underline("change the variable by sight")#