Chapter 5: Q. 398 (page 683)

In the following exercises, solve each system of equations. Use either substitution or elimination.
$2 x + 3 y = 12 - 4 x + 6 y = - 16$

Short Answer

Expert verified

$x = 5 and y = \frac{2}{3}$

Step by step solution

Step 1. Given Information

In the given exercises we have to solve given system of equations using either substitution or elimination method.

$2 x + 3 y = 12 - 4 x + 6 y = - 16$

Step 2. Solve the equations

$2 x + 3 y = 12 \dots \dots \dots \dots \dots \dots \dots Equation 1 - 4 x + 6 y = - 16 \dots \dots \dots \dots \dots Equation 2$

Using the elimination method to solve the equation.

Multiply the Equation 1 by 2

$2 (2 x + 3 y) = 12 \times 2 4 x + 6 y = 24 \dots \dots \dots \dots \dots \dots \dots Equation 3$

Add Equation 3 and Equation 2.

$4 x + 6 y - 4 x + 6 y = 24 - 16 12 y = 8 y = \frac{8}{12} y = \frac{2}{3}$

Now substitute $y = \frac{2}{3} in 2 x + 3 y = 12$

$2 x + 3 (\frac{2}{3}) = 12 2 x + 2 = 12 2 x = 12 - 2 2 x = 10 x = 5$

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In the following exercises, solve each system of equations. Use either substitution or elimination.
$2 x + 3 y = 12 - 4 x + 6 y = - 16$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Solve the equations

Add Equation 3 and Equation 2.

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In the following exercises, solve each system of equations. Use either substitution or elimination.2x+3y=12−4x+6y=−16

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Solve the equations

Add Equation 3 and Equation 2.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Decision Maths

Mechanics Maths

Discrete Mathematics

Calculus

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In the following exercises, solve each system of equations. Use either substitution or elimination.
$2 x + 3 y = 12 - 4 x + 6 y = - 16$