Chapter 4: Q 4.10 (page 374)

Solve the system by graphing: $\{\begin{cases} y = \frac{1}{2} x - 4 \\ 2 x - 4 y = 16 \end{cases}$

Short Answer

Expert verified

The system of equations $\{\begin{cases} y = \frac{1}{2} x - 4 \\ 2 x - 4 y = 16 \end{cases}$ has infinitely many solutions and it can be seen in the graph as

Step by step solution

Step 1. Given Information.

We are given a system of equations $\{\begin{cases} y = \frac{1}{2} x - 4 \\ 2 x - 4 y = 16 \end{cases}$ and we need to find its solution by graphing.

Step 2. Graph the first equation.

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

So its graph is given as,

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

Solving the equation $2 x - 4 y = 16$ for $y$ we get,

localid="1644388026323" $\begin{array}{rcl} 2 x - 4 y - 2 x & = & 16 - 2 x \\ - 4 y & = & - 2 x + 16 \\ \frac{- 4 y}{- 4} & = & \frac{- 2 x + 16}{- 4} \\ y & = & \frac{1}{2} x - 4 \end{array}$

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

So its 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 graph of the equations is the same.
Since every point on the line makes both equations true, there are infinitely many ordered pairs that make both equations true.
There are infinitely many solutions to this system.

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Solve the system by graphing: $\{\begin{cases} y = \frac{1}{2} x - 4 \\ 2 x - 4 y = 16 \end{cases}$

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=12x-42x-4y=16

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

Pure Maths

Calculus

Mechanics Maths

Statistics

Theoretical and Mathematical Physics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Solve the system by graphing: $\{\begin{cases} y = \frac{1}{2} x - 4 \\ 2 x - 4 y = 16 \end{cases}$