Chapter 4: Q. 54 (page 386)

In the following exercises, solve the systems of equations by elimination.
$3 x + 8 y = 67 5 x + 3 y = 60$

Short Answer

Expert verified

The solution for the system of linear equation is $(9, 5)$ .

Step by step solution

Step 1. Given Information

The system of linear equations:

$3 x + 8 y = 67 . . . . . . . . (1) 5 x + 3 y = 60 . . . . . . . . (2)$

Step 2. Calculation

Here both equations are in standard form. To get opposite coefficients of y multiply first equation with 3.

$3 (3 x + 8 y) = 3 (67) 9 x + 24 y = 201 . . . . . . . . (3)$

Also multiply second equation with $- 8$ .

$- 8 (5 x + 3 y) = - 8 (60) - 40 x - 24 y = - 480 . . . . . . . . (4)$

Solve for x:

From equations $(3)$ and $(4)$ :

$9 x + 24 y = 201 - 40 x - 24 y = - 480 - 31 x = - 279 x = \frac{- 279}{- 31} x = 9$

Solve for y:

Substitute $x = 9$

in the equation $3 x + 8 y = 67$ and solve for y.

$3 x + 8 y = 67 3 (9) + 8 y = 67 27 + 8 y = 67 8 y = 67 - 27 8 y = 40 y = \frac{40}{8} y = 5$

The solution for the system of linear equation is $(9, 5)$ .

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In the following exercises, solve the systems of equations by elimination.
$3 x + 8 y = 67 5 x + 3 y = 60$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Calculation

One App. One Place for Learning.

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In the following exercises, solve the systems of equations by elimination.3x+8y=675x+3y=60

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Logic and Functions

Probability and Statistics

Calculus

Geometry

Statistics

Study anywhere. Anytime. Across all devices.

In the following exercises, solve the systems of equations by elimination.
$3 x + 8 y = 67 5 x + 3 y = 60$