How do you solve x-2y=2x−2y=2 and y^2-x^2=2x+4y2−x2=2x+4?
1 Answer
Mar 24, 2015
The logic behind solving by substitution is expressing the given equation in two variables (say x and y) in terms of only one variable (i.e. make only x or y appear as the variable in the equation).
Usually, you will be given two equations that have been expressed in terms of two variables. Do not panic!
- Rearrange one of them to express one of the variables in terms of the other. Usually, it is easier to select a linear equation for this purpose.
In this case, writex-2y=2x−2y=2 asx=2+2yx=2+2y . Note that we had to add 2y on both sides of the equation to get that result. - Substitute the value of x into the other equation so that you get an expression in terms of y.
Soy^2-x^2=2x+4y2−x2=2x+4 becomesy^2-(2+2y)^2=2(2+2y)+4y2−(2+2y)2=2(2+2y)+4
=>⇒ y^2 - (4+8y+4y^2)=4+4y+4y2−(4+8y+4y2)=4+4y+4
=>⇒ -3y^2 -4-8y=8+4y−3y2−4−8y=8+4y
=>⇒ -3y^2 -12-12y=0−3y2−12−12y=0
=>⇒ y^2+4y+4=0y2+4y+4=0 (Taking -3 as the common factor)
=>⇒ (y+2)^2=0(y+2)2=0
=>⇒ y=-2y=−2 - Resubstitute the value of y into the original linear equation to get the value of x.
Sox=2-4x=2−4 =>⇒ x=-2x=−2
