Chapter 5: Q. 396 (page 683)

In the following exercises, solve each system of equations. Use either substitution or elimination.
$4 x - 3 y = 7 5 x - 2 y = 0$

Short Answer

Expert verified

The solution set is $(\frac{14}{23}, - \frac{105}{69})$ .

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.

$4 x - 3 y = 7 5 x - 2 y = 0$

Step 2. 4x−3y=7………………Equation 15x−2y=0………………Equation 2

Using elimination method to solve the equation.

Multiply Equation 1 by $2$ .

role="math" localid="1647882895912" $2 (4 x - 3 y) = 7 \times 2 8 x - 6 y = 14 \dots \dots \dots \dots \dots \dots \dots Equation 3$

Step 3. Multiply Equation 2 by 3.

$3 (5 x - 2 y) = 0 \times 3 15 x - 6 y = 0 \dots \dots \dots \dots \dots \dots \dots Equation 4$

Step 4. Add Equation 3 and Equation 4 to eliminate y.

$8 x - 6 y + 15 x - 6 y = 14 + 0 23 x = 14 Divide by 23 on both side \frac{23}{23} x = \frac{14}{23} x = \frac{14}{23}$

Step 5. Putting the value of x in the Equation 1

$4 \times \frac{14}{23} - 3 y = 7 \frac{56}{23} - 3 y = 7 Subtract \frac{56}{23} on both side \frac{56}{23} - 3 y - \frac{56}{23} = 7 - \frac{56}{23} - 3 y = 7 \times \frac{23}{23} - \frac{56}{23} - 3 y = \frac{161}{23} - \frac{56}{23} - 3 y = \frac{161 - 56}{23} - 3 y = \frac{105}{23} \frac{- 3}{- 3} y = \frac{1}{- 3} \times \frac{105}{23} y = - \frac{105}{69}$

The solution set is $(\frac{14}{23}, - \frac{105}{69})$

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In the following exercises, solve each system of equations. Use either substitution or elimination.
$4 x - 3 y = 7 5 x - 2 y = 0$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. 4x−3y=7………………Equation 15x−2y=0………………Equation 2

Step 3. Multiply Equation 2 by 3.

Step 4. Add Equation 3 and Equation 4 to eliminate y.

Step 5. Putting the value of x in the Equation 1

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In the following exercises, solve each system of equations. Use either substitution or elimination.4x−3y=75x−2y=0

Short Answer

Step by step solution

Step 1. Given Information

Step 2. 4x−3y=7………………Equation 15x−2y=0………………Equation 2

Step 3. Multiply Equation 2 by 3.

Step 4. Add Equation 3 and Equation 4 to eliminate y.

Step 5. Putting the value of x in the Equation 1

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Discrete Mathematics

Statistics

Decision Maths

Theoretical and Mathematical Physics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

In the following exercises, solve each system of equations. Use either substitution or elimination.
$4 x - 3 y = 7 5 x - 2 y = 0$