Answer to Question #340008 in Algebra for nixx

Question

11. Solve the system by using the substitution method:

y=(x+3)²-1

y=2x+5

A. (-3,-1) and (-1,3)

B. (-1,-3) and (3,-1)

C. (-3,1),(-1,3),(-1,-3) and (3,-1)

D.No solution! it is an inconsistent system

12. Solve the system by using the elimination method:

3x+y²=21

4x²-2y³=-2

A. (2,3) and (2,-3)

B. (-2,3) and (-2,-3)

C. (2,3),(2,-3),(-2,3) and (-2,-3)

D. No solution! It is an Inconsistent System

Answer 1

11.

$$y=2x+5$$

$$y=2x+5$$ $$2x+5=(x+3)^2-1$$

Solve the equation

$$2x+5=x^2+6x+9-1$$

$$x^2+4x+3=0$$

$$(x+3)(x+1)=0$$

$x_1=-3, x_2=-1$

Plug solution back into the first equation.

$$x_1=-3: y_1=2(-3)+5=-1$$

$$x_2=-1: y_2=2(-1)+5=3$$

A. (-3,-1) and (-1,3)

12.

$$3x+y^2=21$$ $$4x^3-2y^3=-2$$

Given system cannot be solved by using the elimination method.

I think the task is not correct.

If the system is

$$3x^2+y^2=21$$ $$4x^2-2y^2=-2$$

then

$$6x^2+2y^2=42$$ $$4x^2-2y^2=-2$$

$$3x^2+y^2=21$$ $$4x^2-2y^2+6x^2+2y^2=-2+42$$

$$3x^2+y^2=21$$ $$10x^2=40$$

$$3(4)+y^2=21$$ $$x^2=4$$

$$y^2=9$$ $$x^2=4$$

C. (2,3),(2,-3),(-2,3) and (-2,-3)