Solve the nonlinear system of equations
1 answer:
Answer:
There are no real solutions. The complex solutions are ...
(x, y) = (2.5-i√1.75, -2.5+i√1.75) or (2.5+i1.75, -2.5-i1.75)
Step-by-step explanation:
Subtract the first equation from the second.
y -y = (x^2 -6x +8) -(-x)
0 = x^2 -5x +8
Rewrite to facilitate completing the square:
x^2 -5x = -8
x^2 -5x +6.25 = -1.75 . . . . . add 6.25 to complete the square
(x -2.5)^2 = -1.75 . . . . . write as a square
x -2.5 = ±i√1.75 . . . . . . take the square root
x = 2.5 ± i√1.75 . . . . . . add 2.5; y is the opposite of this
Solutions are ...
- x = 2.5 +i√1.75, y = -2.5 -i√1.75
- x = 2.5 -i√1.75, y = -2.5 +i√1.75
_____
The graph shows the equations have no point of intersection, meaning there are no real solutions. The complex solutions are shown above.
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Hi<span>, Victoriasoto93p63zva!
To rewrite these equations in standard form you need to understand that standard form looks something like this Ax+By=C, now obviously there will be variations like </span>Ax-By=C or -Ax+By=C, etc..., but for these expressions, they would look like this:
<span>1. -8y + 0x = 37
2. 14x </span>+ 4y<span> = -18
3. x + </span>
y = 
<span>
4. 13x + 0y = -25
-</span><span>ASIAX</span><span> </span><span>Frequent Answerer</span>
To rewrite these equations in standard form you need to understand that standard form looks something like this Ax+By=C, now obviously there will be variations like </span>Ax-By=C or -Ax+By=C, etc..., but for these expressions, they would look like this:
<span>1. -8y + 0x = 37
2. 14x </span>+ 4y<span> = -18
3. x + </span>
4. 13x + 0y = -25
-</span><span>ASIAX</span><span> </span><span>Frequent Answerer</span>