17. Solve the following system of equations algebraically. 3x-5y+2z = -S 5x + y+ 6z = 33 -2x +10y-3z = 40 18. One application of solving a system of three linear equations is, somewhat ironically, in algebraícally finding the equation of a parabola in standard form. Given a parabola that passes through the points (-4.5).(-1,-10), and (2,11): (a) Substitute each point into the general form y = ax' +bx+ c, to produce three equations with the three unknowns a, b, and c. The first is done for you. 5 = a(-4) +b(-4)+c5 =16a -4b+c (b) Solve this system for a, b, and c and state the equation of the parabola.
17. Solve the following system of equations algebraically. 3x-5y+2z = -S 5x + y+ 6z = 33 -2x +10y-3z = 40 18. One application of solving a system of three linear equations is, somewhat ironically, in algebraícally finding the equation of a parabola in standard form. Given a parabola that passes through the points (-4.5).(-1,-10), and (2,11): (a) Substitute each point into the general form y = ax' +bx+ c, to produce three equations with the three unknowns a, b, and c. The first is done for you. 5 = a(-4) +b(-4)+c5 =16a -4b+c (b) Solve this system for a, b, and c and state the equation of the parabola.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![**Educational Content: Solving Systems of Equations**
**17. Solve the following system of equations algebraically:**
\[
\begin{align*}
3x - 5y + 2z &= -5 \\
5x + y + 6z &= 33 \\
-2x + 10y - 3z &= 40 \\
\end{align*}
\]
**18. Parabola Equation from Three Points:**
One application of solving a system of three linear equations is, somewhat ironically, in algebraically finding the equation of a parabola in standard form. Given a parabola that passes through the points \((-4, 5)\), \((-1, -10)\), and \( (2, 11) \):
(a) Substitute each point into the general form \(y = ax^2 + bx + c\), to produce three equations with the three unknowns \(a\), \(b\), and \(c\). The first is done for you:
\[
5 = a(-4)^2 + b(-4) + c \Rightarrow 5 = 16a - 4b + c
\]
(b) Solve this system for \(a\), \(b\), and \(c\) and state the equation of the parabola.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff874369a-1501-4297-ae95-de7ae7d9f557%2Fb4a29d17-4f4a-40cc-adf1-f4929a2e9c5e%2Fnaeopc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Educational Content: Solving Systems of Equations**
**17. Solve the following system of equations algebraically:**
\[
\begin{align*}
3x - 5y + 2z &= -5 \\
5x + y + 6z &= 33 \\
-2x + 10y - 3z &= 40 \\
\end{align*}
\]
**18. Parabola Equation from Three Points:**
One application of solving a system of three linear equations is, somewhat ironically, in algebraically finding the equation of a parabola in standard form. Given a parabola that passes through the points \((-4, 5)\), \((-1, -10)\), and \( (2, 11) \):
(a) Substitute each point into the general form \(y = ax^2 + bx + c\), to produce three equations with the three unknowns \(a\), \(b\), and \(c\). The first is done for you:
\[
5 = a(-4)^2 + b(-4) + c \Rightarrow 5 = 16a - 4b + c
\]
(b) Solve this system for \(a\), \(b\), and \(c\) and state the equation of the parabola.
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