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Solve each system of equations; nonlinear algebra 2

x2 + x + y - 26 = 0
x + y = 1

User Kynth
by
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1 Answer

4 votes

Answer:

(5,-4) and (-5,6)

Explanation:

Given:


\left\{\begin{array}{l}x^2+x+y-26=0\\ \\x+y=1\end{array}\right.

Solve it. First, express y in terms of x from the second equation:


y=1-x

Substitute it into the first equation:


x^2+x+1-x-26=0\\ \\x^2-25=0\\ \\(x-5)(x+5)=0

Apply zero product property:


x-5=0\ \text{or}\ x+5=0

So,


x=5\ \text{or}\ x=-5

When
x=5, then
y=1-5=-4

When
x=-5, then
y=1-(-5)=6

We get two solutions: (5,-4) and (-5,6)

User Wfjm
by
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