preprekomW

2021-06-12

Substitution and elimination, and matrix methods such as the Gauss-Jordan method and Cramer's rule. Use each method at least once when solving the systems below. include solutions with nonreal complex number components. For systems with infinitely many solutions, write the solution set using an arbitrary variable.
$y={x}^{2}+6x+9$
$x+y=3$

$y={x}^{2}+6x+9$ (1)
$x+y=3$
Substitute eq 2 ... eq 1.
$3-x={x}^{2}+6x+9$
On simplification $\to 3-x-{x}^{2}-6x-9=0$
${x}^{2}+7x+6=0$
Factor $\to$ $\left(x+1\right)\left(x+6\right)=0$
Applying zero factor properly $x+1=0$ or $x+6=0$
$x=-1$ or $x=-6$
putting value of x in eq 2.
$y=3-\left(-1\right),y=4$ or $y=3-\left(-6\right),y=9$
Solution set $=\left\{\left(-1,4\right)\left(-6,9\right)\right\}$

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