Certainly! Let's solve the system of equations step-by-step to find the solution points:
Given the system of equations:
[tex]\[
\begin{array}{l}
y = 2x^2 - 12x + 20 \\
y = 2
\end{array}
\][/tex]
1. Set the equations equal to each other:
Since both expressions are equal to [tex]\( y \)[/tex], set them equal to each other:
[tex]\[
2x^2 - 12x + 20 = 2
\][/tex]
2. Simplify the equation:
Subtract 2 from both sides to set the equation to zero:
[tex]\[
2x^2 - 12x + 18 = 0
\][/tex]
3. Solve the quadratic equation:
We reduce this by dividing every term by 2:
[tex]\[
x^2 - 6x + 9 = 0
\][/tex]
This is a simple quadratic equation. Factorizing, we get:
[tex]\[
(x - 3)^2 = 0
\][/tex]
Therefore:
[tex]\[
x = 3
\][/tex]
4. Find the [tex]\( y \)[/tex]-coordinate:
Substitute [tex]\( x = 3 \)[/tex] back into either of the original equations (easier to use [tex]\( y = 2 \)[/tex]):
[tex]\[
y = 2
\][/tex]
So, the solution point for the given system of equations is:
[tex]\[
(3, 2)
\][/tex]
5. Plotting the Solution Point:
Now, using the drawing tools mentioned: The solution point is [tex]\((3, 2)\)[/tex] on the graph. Simply plot the point at coordinates [tex]\((3, 2)\)[/tex] on the given graph.
To summarize, the solution involves aligning the curves [tex]\( y = 2x^2 - 12x + 20 \)[/tex] and [tex]\( y = 2 \)[/tex], which intersect at exactly one point: [tex]\( (3, 2) \)[/tex]. Go ahead and plot this point on your graph.
