Search 82,062 tutors
Ask a question
0 0

solve using substitution y^2=x and x+2y+3=0

Tutors, please sign in to answer this question.

2 Answers

If y^2=x, then you can substitute y^2 for x in the second equation, giving you y^2+2y+3=0.  Now that there's but a single variable (y), you should be able to solve as usual for y.  Once you have y, plug that number(s) into y^2=x and you'll have x.
The substitution method simply means that, given two equations, one can be reduced into a definitional statement, an equation that just tells you how to express one variable in terms of the other (in other words, an equation that starts with something like "x=" or ends with "=y").  You then substitute whatever's in the complicated side of this equation for the whichever variable is on the simple side in the OTHER equation, at which point you have a normal, one-variable version of the equation.


y2 = x
x + 2y + 3 = 0
Substitute y2 in place of x in the second equation, solve for y::
y2 + 2y + 3 = 0
Use the quadratic formula:
y = [-2 ± √(22-4*1*3)]/2
y = -1 ± i√2
Solve for x:
x = y2 = [-1 ± i√2]2
x = 1-i2√2, -1+ i2√2