Give all solutions of the nonlinear system of equations, including those with nonreal complex components.
$\begin{array} { l }
y = x ^ { 2 } - 14 x + 49 \
x + y = 19
\end{array}$
A) {(3,22),(10,9)}
B) {(3,16),(10,9)}
C) {(7,12)}
D) {(-3,22),(-10,29)}

Question

Give all solutions of the nonlinear system of equations, including those with nonreal complex components.
$\begin{array} { l } 
y = x ^ { 2 } - 14 x + 49 \
x + y = 19
\end{array}$
A) {(3,22),(10,9)} 
B) {(3,16),(10,9)} 
C) {(7,12)} 
D) {(-3,22),(-10,29)}

Quizplus · Accepted Answer

The first equation simplifies to $y = (x-7)^2$. Substituting into the second equation gives $x + (x-7)^2 = 19$. Solving this quadratic equation yields solutions $x = 3$ and $x = 10$. Substituting back gives corresponding $y$ values of 16 and 9, respectively.

Give All Solutions of the Nonlinear System of Equations, Including y=x2−14x+49x+y=19\begin{array} { l } y = x ^ { 2 } - 14 x + 49 \\x + y = 19\end{array}y=x2−14x+49x+y=19​

Give All Solutions of the Nonlinear System of Equations, Including $\begin{array} { l } y = x ^ { 2 } - 14 x + 49 \\x + y = 19\end{array}$