Answer to Question #340008 in Algebra for nixx

Question #340008

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


1
Expert's answer
2022-05-16T10:11:18-0400

11.


y=2x+5y=2x+5


y=2x+5y=2x+52x+5=(x+3)212x+5=(x+3)^2-1

Solve the equation


2x+5=x2+6x+912x+5=x^2+6x+9-1

x2+4x+3=0x^2+4x+3=0

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

x1=3,x2=1x_1=-3, x_2=-1

Plug solution back into the first equation.


x1=3:y1=2(3)+5=1x_1=-3: y_1=2(-3)+5=-1

x2=1:y2=2(1)+5=3x_2=-1: y_2=2(-1)+5=3

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


12.



3x+y2=213x+y^2=214x32y3=24x^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


3x2+y2=213x^2+y^2=214x22y2=24x^2-2y^2=-2

then


6x2+2y2=426x^2+2y^2=424x22y2=24x^2-2y^2=-2


3x2+y2=213x^2+y^2=214x22y2+6x2+2y2=2+424x^2-2y^2+6x^2+2y^2=-2+42


3x2+y2=213x^2+y^2=2110x2=4010x^2=40


3(4)+y2=213(4)+y^2=21x2=4x^2=4


y2=9y^2=9x2=4x^2=4

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


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