Chapter 4: Q 4.7 (page 373)

Solve the system by graphing: $\{\begin{cases} y = - \frac{1}{4} x + 2 \\ x + 4 y = - 8 \end{cases}$

Short Answer

Expert verified

The system of equations $\{\begin{cases} y = - \frac{1}{4} x + 2 \\ x + 4 y = - 8 \end{cases}$ has no solution and it can be seen in the graph as,

Step by step solution

Step 1. Given Information.

We are given a system of equations $\{\begin{cases} y = - \frac{1}{4} x + 2 \\ x + 4 y = - 8 \end{cases}$ and we need to find its solution by graphing.

Step 2. Graph the first equation.

The equation $y = - \frac{1}{4} x + 2$ is in slope-intercept form, so its slope is $- \frac{1}{4}$ and its $y$ intercept is $2$ .

So its graph is given as

Step 3. Graph the second equation on the same rectangular coordinate system.

Solving the equation $x + 4 y = - 8$ for $y$ we get,

localid="1644386022551" $\begin{array}{rcl} x + 4 y - x & = & - 8 - x \\ 4 y & = & - x - 8 \\ \frac{4 y}{4} & = & \frac{- x - 8}{4} \\ y & = & - \frac{1}{4} x - 2 \end{array}$

So the slope of the line is $- \frac{1}{4}$ and its $y$ intercept is 2.

So the graph can be drawn on the same plane as,

Step 4. Identify the solution to the system.

From the graph, it can be seen that the lines are parallel.
Since no point is on both lines, there is no ordered pair that makes both equations true.
There is no solution to the given system.

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Solve the system by graphing: $\{\begin{cases} y = - \frac{1}{4} x + 2 \\ x + 4 y = - 8 \end{cases}$

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Graph the first equation.

Step 3. Graph the second equation on the same rectangular coordinate system.

Step 4. Identify the solution to the system.

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Solve the system by graphing:y=-14x+2x+4y=-8

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Graph the first equation.

Step 3. Graph the second equation on the same rectangular coordinate system.

Step 4. Identify the solution to the system.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Discrete Mathematics

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Study anywhere. Anytime. Across all devices.

Solve the system by graphing: $\{\begin{cases} y = - \frac{1}{4} x + 2 \\ x + 4 y = - 8 \end{cases}$