Question #95527

1 Answer
Jan 4, 2018

Answer:

#{(x = -3), (y = -4) :}#

Explanation:

Start by dividing both sides of the second equation by #-2#. You will end up with

#(2y)/(-2) = 7/-2 + (5x)/-2#

#-y = -7/2 - (5x)/2#

Now, notice that the left-hand side of the two equations is equal.

#{( -y = -5/7 - (11x)/7), (-y = -7/2 - (5x)/2) :}#

This means that you can equate the two right-hand sides to get an equation with one unknown, #x#.

#-5/7 - (11x)/7 = -7/2 - (5x)/2#

DIvide or multiply both sides by #-1# to get rid of the minus signs.

#5/7 + (11x)/7 = 7/2 + (5x)/2#

#(5 + 11x)/7 = (7 + 5x)/2#

Next, cross multiply, i.e. multiply the numerator of one fraction by the denominator of the second fraction and vice versa. You will end up with

#7 * (7 + 5x) = 2 * (5 + 11x)#

This will be equivalent o

#49 + 35x = 10 + 22x#

Subtract #22x# and #49# from both sides to get

#13x = - 39#

Finally, divide both sides by #13# to isolate #x#

#x = -39/13 = -3#

Now that you have a value for #x#, pick one of the two equations and use it to find the value of #y#.

#2y = 7 + 5 * (-3)#

#2y = -8#

Divide both sides by #2# to isolate #y#

#y = -4#

Therefore, your system of two equations with two unknowns has the solution set

#{(x = -3), (y = -4) :}#

If you want, you can double-check the result by plugging in the two values into the original equations.

You will have

#-(-4) = -5/7 - (11 * (-3))/7#

#4 = (-5 + 33)/7" "color(green)(sqrt())#

and

#2 * (-4) = 7 + 5 * (-3)#

#-8 = 7 - 15" "color(green)(sqrt())#