Chapter 5: Q. 142 (page 626)

Solve a System of Equations by Elimination -
$5 x - 3 y = - 1 2 x - y = 2$

Short Answer

Expert verified

The simplification of Expression will be - $(7, 12)$ .

Step by step solution

Step 1. Given Information.

Equation - $5 x - 3 y = - 1 2 x - y = 2$

Step 2. To Find

Solve a System of Equations by Elimination and find the value of x and y.

Step 3. Explanation

Equation -

$5 x - 3 y = - 1 2 x - y = 2$

We can eliminate y's by multiplying the second equation by 3 -

$5 x - 3 y = - 1 (2 x - y) \times 3 = 2 \times 3 5 x - 3 y = - 1 6 x - 3 y = 6$

Step 4. Calculation

The equation become -

$5 x - 3 y = - 1 6 x - 3 y = 6$

We subtract the x's and y's and constants -

$\begin{array}{l} 5 x - 3 y = - 1 \\ \frac{6 x - 3 y = 6}{- x = - 7} \end{array}$

Solve for x -

$x = 7$

Substitute $x = 7$ into the second equation $2 x - y = 2$ , Then Solve for y -

$2 x - y = 2 2 \times 7 - y = 2 14 - y = 2 - y = 2 - 14 y = 12$

Written as $(x, y)$ will be $(7, 12)$

Step 5. Check the answer

Check that the ordered pair is a solution to both original equations -

Put $(7, 12)$ in the equations -

$5 x - 3 y = - 1 5 \times 7 - 3 \times 12 = - 1 35 - 36 = - 1 - 1 = - 1$

$2 x - y = 2 2 \times 7 - 12 = 2 14 - 12 = 2 2 = 2$

The Solution is - $(7, 12)$

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Solve a System of Equations by Elimination -
$5 x - 3 y = - 1 2 x - y = 2$

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. To Find

Step 3. Explanation

Step 4. Calculation

Step 5. Check the answer

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Solve a System of Equations by Elimination -5x-3y=-12x-y=2

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. To Find

Step 3. Explanation

Step 4. Calculation

Step 5. Check the answer

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Discrete Mathematics

Geometry

Calculus

Statistics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Solve a System of Equations by Elimination -
$5 x - 3 y = - 1 2 x - y = 2$