/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 9 Solve each system by graphing. C... [FREE SOLUTION] | 91影视

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Chapter 7: Problem 9

Solve each system by graphing. Check the coordinates of the intersection point in both equations. \(\left\\{\begin{array}{l}y=x+5 \\ y=-x+3\end{array}\right.\)

Short Answer

Expert verified
The solution of this system of equations by graphing is \(-1, 4\). After checking this point in both equations, it's clear that it is indeed the correct solution.

Step by step solution

01

Plot the first equation

Firstly, the equation \(y=x+5\) is plotted on the graph. This line has a slope of 1 and it crosses the y-axis at 5.
02

Plot the second equation

Next, the equation \(y=-x+3\) is also plotted on the same graph. This line has a slope of -1 and it crosses the y-axis at 3.
03

Find intersection point

The solution to the system is the coordinates of the point at which the two lines intersect. After plotting both equations, it's clear that they intersect at the point \(-1, 4\), and this is therefore the solution of the system.
04

Check intersection point

Substitute \(-1\) for \(x\) and \(4\) for \(y\) into both equations to check. For the first equation: \(y = -1 + 5 = 4\) and for the second equation: \(y = --1 + 3 = 4\). Since the results are true for both equations, the solution is valid.

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Most popular questions from this chapter

Graph the solution set of each system of inequalities. \(\left\\{\begin{array}{l}4 x-5 y \geq-20 \\ x \geq-3\end{array}\right.\)

A ball is thrown upward and outward from a height of 6 feet. The table shows four measurements indicating the ball's height at various horizontal distances from where it was thrown. The graphing calculator screen displays a quadratic function that models the ball's height, \(y\), in feet, in terms of its horizontal distance, \(x\), in feet. $$ \begin{array}{|c|c|} \hline \begin{array}{c} \boldsymbol{x} \text {, Ball's } \\ \text { Horizontal } \\ \text { Distance } \\ \text { (feet) } \end{array} & \begin{array}{c} \boldsymbol{y}, \\ \text { Ball's } \\ \text { Height } \\ \text { (feet) } \end{array} \\ \hline 0 & 6 \\ \hline 1 & 7.6 \\ \hline 3 & 6 \\ \hline 4 & 2.8 \\ \hline \end{array} $$ $$ \begin{aligned} &\text { [adadReg }\\\ &\begin{aligned} &y=3 \times 2+b x+c \\ &\bar{y}=.8 \\ &b=2.4 \\ &c=6 \end{aligned} \end{aligned} $$ a. Explain why a quadratic function was used to model the data. Why is the value of \(a\) negative? b. Use the graphing calculator screen to express the model in function notation. c. Use the model from part (b) to determine the \(x\)-coordinate of the quadratic function's vertex. Then complete this statement: The maximum height of the ball occurs ____ feet from where it was thrown and the maximum height is ____ feet.

a. Create a scatter plot for the data in each table. b. Use the shape of the scatter plot to determine if the data are best modeled by a linear function, an exponential function, a logarithmic function, or a quadratic function. $$ \begin{array}{|c|c|} \hline \boldsymbol{x} & \boldsymbol{y} \\ \hline 0 & -3 \\ \hline 1 & 2 \\ \hline 2 & 7 \\ \hline 3 & 12 \\ \hline 4 & 17 \\ \hline \end{array} $$

Graph each linear inequality. \(x \geq 0\)

A ball is thrown upward and outward from a height of 6 feet. The table shows four measurements indicating the ball's height at various horizontal distances from where it was thrown. The graphing calculator screen displays a quadratic function that models the ball's height, \(y\), in feet, in terms of its horizontal distance, \(x\), in feet. $$ \begin{array}{|c|c|} \hline \begin{array}{c} \boldsymbol{x}, \text { Ball's } \\ \text { Horizontal } \\ \text { Distance } \\ \text { (feet) } \end{array} & \begin{array}{c} \boldsymbol{y}, \\ \text { Ball's } \\ \text { Height } \\ \text { (feet) } \end{array} \\ \hline 0 & 6 \\ \hline 0.5 & 7.4 \\ \hline 1.5 & 9 \\ \hline 4 & 6 \\ \hline \end{array} $$ $$ \begin{array}{|l|} \hline u a d R e g \\ y=a \times 2+b x+c \\ a=-.8 \\ b=3.2 \\ c=6 \end{array} $$ a. Explain why a quadratic function was used to model the data. Why is the value of \(a\) negative? b. Use the graphing calculator screen to express the model in function notation. c. Use the model from part (b) to determine the \(x\)-coordinate of the quadratic function's vertex. Then complete this statement: The maximum height of the ball occurs _____ feet from where it was thrown, and the maximum height is _____ feet.
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