Chapter 5: Q. 30 (page 595)

In the following exercises, solve the following systems of equations by graphing.
$\{\begin{cases} 2 x - y = 4 \\ 2 x + 3 y = 12 \end{cases}$

Short Answer

Expert verified

The solutions to the system of equations are $x = 3$ and $y = 2 .$

Step by step solution

Step 1. Given information.

We have:

$\{\begin{cases} 2 x - y = 4 \\ 2 x + 3 y = 12 \end{cases}$

Step 2. Find the intercepts.

We will find the x-intercept and y-intercept of both equations and use them to graph the lines.

The system of equations are:

$\{\begin{cases} 2 x - y = 4 \\ 2 x + 3 y = 12 \end{cases}$

x-intercept: substitute $y = 0$

$2 x - 0 = 4 x = 2$

X-intercept: $(2, 0)$

$2 x + 3 (0) = 12 x = 6$

X-intercept: $(6, 0)$

y-intercept: substitute $x = 0$

$2 (0) - y = 4 y = - 4$

Y-intercept: $(0, - 4)$

$2 (0) + 3 y = 12 y = 4$

Y-intercept: $(0, 4)$

Step 3. Use the intercept to draw the graph.

Graph the line and find the intersection point:

The lines intersect at $(3, 2)$ .

Therefore, the solutions are:

$x = 3, y = 2$

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In the following exercises, solve the following systems of equations by graphing.
$\{\begin{cases} 2 x - y = 4 \\ 2 x + 3 y = 12 \end{cases}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the intercepts.

Step 3. Use the intercept to draw the graph.

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In the following exercises, solve the following systems of equations by graphing.2x-y=42x+3y=12

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the intercepts.

Step 3. Use the intercept to draw the graph.

One App. One Place for Learning.

Most popular questions from this chapter

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In the following exercises, solve the following systems of equations by graphing.
$\{\begin{cases} 2 x - y = 4 \\ 2 x + 3 y = 12 \end{cases}$