Question

Solve each system of equations; nonlinear algebra 2

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

Answer 1

(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)