Question

name
4-1 additional practice
solving systems of equations by graphing
use a graph to solve each system of equations. list the solution.

1. {y = 2x - 1, y = -4x - 7}
2. {18x - 3y = 21, y = 6x - 7}
3. {y = 6x + 4, 6x - y = 1}

use a graph to approximate the solution of each system. list the estimated solution.

1. {y = 5x - 3, y = -3x + 4}
2. {y = 4x - 3, y = 8x - 5}
3. {y = -3x + 7, x - 2y = -6}
4. can there be more than one point of intersection between the graphs of two linear equations? explain.
5. elena and marcus jog after school each day. one day, elena and marcus jogged a total of 15 miles. elena jogged 1 mile more than marcus. use a graph to find the number of miles each person jogged.

Explanation:

Step1: Recall graph - intersection concept

The solution of a system of linear equations is the point of intersection of their graphs.

Step2: Analyze question 7

Two distinct non - parallel lines intersect at exactly one point. Parallel lines have the same slope and either do not intersect (different y - intercepts) or are the same line (same y - intercept, infinite solutions). So, two distinct linear equations (non - parallel) have exactly one intersection point.

Step3: Solve question 8

Let $x$ be the number of miles Marcus jogged and $y$ be the number of miles Elena jogged. We have the system of equations:

$$\begin{cases}x + y=15\\y=x + 1\end{cases}$$

Substitute $y=x + 1$ into $x + y=15$:
$x+(x + 1)=15$
$2x+1 = 15$
$2x=14$
$x = 7$
Since $y=x + 1$, then $y=7 + 1=8$

Answer:

1. No. Two distinct non - parallel lines intersect at exactly one point. Parallel lines either do not intersect (different y - intercepts) or are the same line (infinite solutions).
2. Marcus jogged 7 miles and Elena jogged 8 miles.