Question

question #3
true or false. the point given is a solution to the system of equations
-x^2 - 3x - y+3 = 0
x + y - 4 = 0
point: (-1,5)
o false
o true
question #4
true or false. the point given is a solution to the system of equations.
-2x^2 - 11x + y + 5 = 0
x - y + 5 = 0
point (0, -5)
o false
o true

Explanation:

Step1: Substitute into first - equation of Question #3

Substitute \(x=-1\) and \(y = 5\) into \(-x^{2}-3x - y+3\).
\[

$$\begin{align*} -(-1)^{2}-3\times(-1)-5 + 3&=-1 + 3-5 + 3\\ &=(-1-5)+(3 + 3)\\ &=-6 + 6\\ &=0 \end{align*}$$

\]

Step2: Substitute into second - equation of Question #3

Substitute \(x=-1\) and \(y = 5\) into \(x + y-4\).
\[

$$\begin{align*} -1+5-4&=4 - 4\\ &=0 \end{align*}$$

\]

Step3: Substitute into first - equation of Question #4

Substitute \(x = 0\) and \(y=-5\) into \(-2x^{2}-11x + y+5\).
\[

$$\begin{align*} -2\times0^{2}-11\times0-5 + 5&=0+0-5 + 5\\ &=0 \end{align*}$$

\]

Step4: Substitute into second - equation of Question #4

Substitute \(x = 0\) and \(y=-5\) into \(x-y + 5\).
\[

$$\begin{align*} 0-(-5)+5&=0 + 5+5\\ &=10 eq0 \end{align*}$$

\]

Answer:

Question #3: True
Question #4: False