How do you solve #2x+7y=10# and #x-2y=15#?

1 Answer
Aug 5, 2015

Answer:

#{(x = 125/11), (y = -20/11) :}#

Explanation:

You could solve this sytem of equations by multiplication.

More specifically, you can multiply the second equation by #-2# to get

#-2 * (x - 2y) = -2 * 15#

#-2x + 4y = -30#

The two equations now look like this

#{(2x + 7y = 10), (-2x + 4y = -30) :}#

Next, add the left side and the right side of the equations separately to cancel out the #x#-term

#color(red)cancelcolor(black)(2x) + 7y - color(red)cancelcolor(black)(2x) + 4y = 10 + (-30)#

#11y = -20 implies y = color(green)(-20/11)#

Now take this value of #y# and use it in the first equation to find the value of #x#

#2x + 7 * (-20)/11 = 10#

#2x = 10 + 140/11#

#2x = 250/11 implies x = 250/11 * 1/2 = color(green)(125/11)#