Find all solutions of the system of equations. {x−2y=2y2−x2=2x+4

Brittney Lord

Brittney Lord

Answered

2021-09-29

Find all solutions of the system of equations.
{x2y=2y2x2=2x+4

Answer & Explanation

Gennenzip

Gennenzip

Expert

2021-09-30Added 96 answers

Step 1
To find:
The solution of the system of equation.
Given:
The system of equation x2y=2 and y2x2=2x+4.
Calculation:
Simplify the equation x2y=2 as follows:
x2y=2
x=2+2y
Substitute x=2+2y in y2x2=2x+4.
y2(2y+2)2=2(2y+2)+4
y24y248y=4y+4+4
3y2488y4y=0
3y21212y=0
Further simplify as follows:
y2+4y+4=0
(y+2)2=0
y=2
Sbstitute y=2 in x=2+2y.
x=2+2(2)
=24
=2
Step 2
Thus, the solution of the system of equation x=2 and y=2.

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