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Q8.

Expert-verified

Algebra 1

Found in: Page 361

Book edition Student Edition

Author(s) Carter, Cuevas, Day, Holiday, Luchin

Pages 801 pages

ISBN 9780078884801

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Short Answer

Graph each system and determine the number of solutions that it has. If it has one solution, name it.
$\begin{matrix} 2 x + y = - 4 \\ 5 x + 3 y = - 6 \end{matrix}$

The required solution is represented by $(- 6, 8)$ .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Make the required graph and determine the intersection point.

Represent the provided equations in the form of graphs.

Graph of the provided equations are meeting at only one point that is $(- 6, 8)$ .

Step 2. Perform the checking.

The obtained solution is 1 in count that is why the provided equation has only one solution. The obtained point is in the form of $(x, y)$ so perform substitution of the obtained values of x and y into both of the provided equations for checking.

$\begin{array}{l} 2 (- 6) + 8 \overset{?}{=} - 4 \\ - 12 + 8 \overset{?}{=} - 4 \\ - 4 = - 4 True \end{array}$

role="math" localid="1647516856470" $\begin{array}{l} 5 (- 6) + 3 (8) \overset{?}{=} - 6 \\ - 30 + 24 \overset{?}{=} - 6 \\ - 6 = - 6 True \end{array}$

Step 3. Write the conclusion.

As the substitution of obtained solution returns a true statement so it is the required solution.

Most popular questions for Math Textbooks

Graph each system and determine the number of solutions that it has. If it has one solution, name it.

$\begin{matrix} x + y = 8 \\ 3 x + 3 y = 24 \end{matrix}$

On the first day, a total of 40 items were sold for $$ 356$ . Define the variables, and write equations to find the number of cakes and pies sold. Solve by using elimination.

Monarch Middle School
Bake sale
Pies	$$ 10$
Cakes	$$ 8$

State whether each sentence is true or false. If false, replace the underlined term to make a true sentence.

If a consistent system has an infinite number of solutions, it is said to be inconsistent.

Use elimination to solve each system of equations.

$\begin{array}{l} 2 x + y = - 5 \\ x - y = 2 \end{array}$

Use substitution to solve each system of equations.

$\begin{array}{l} 3 x + 2 y = 16 \\ x = 3 y - 2 \end{array}$

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