Answer:
- The first equation is of a parabola
- (x, y) = (-11, 56) or (1, -4)
Step-by-step explanation:
You want a description and solution of the system of equations ...
Description
The first equation is 2nd degree in x and first degree in y. It is the equation of a parabola.
Solution
We can add 5x to the first equation to get ...
5x +y +10 = 10x +x²
Using the second equation to replace (5x +y), we have ...
1 +10 = 10x +x²
x² +10x -11 = 0 . . . . . . . subtract 11 to put in standard form
(x +11)(x -1) = 0 . . . . . . factor
The solutions are the values of x that make these factors zero:
x = -11, or x = 1
The corresponding values of y are ...
y = 1 -5x
y = 1 -5(-11) = 56
y = 1 -5(1) = -4
The solutions are (-11, 56) and (1, -4).
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Additional comment
We find it convenient to use a graphing calculator to solve systems of equations like this. Even when the solutions are fractions or irrational numbers, the graph can be useful.
For a system like this, graphing the function f(x) = x² +5x -11 and identifying its x-intercepts will give you the x-values of the solutions. Then the y-values can be found using either of the original equations.
