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

Question

I need to solve using the substitution method, but i can't figure out how to do it with this problem. y^2 mean y squared.

Answer 1

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.

Answer 2

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