Chapter 5: Q. 145 (page 626)

Solve a System of Equations by Elimination -
$3 x - 5 y = - 9 5 x + 2 y = 16$

Short Answer

Expert verified

The simplification of Expression will be - $(2, 3)$ .

Step by step solution

Step 1. Given Information.

Equation - $3 x - 5 y = - 9 5 x + 2 y = 16$

Step 2. To Find

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

Step 3. Explanation

Equation -

$3 x - 5 y = - 9 5 x + 2 y = 16$

We can eliminate y's by multiplying the first equation by 2 and second equation by 5 -

$(3 x - 5 y) \times 2 = - 9 \times 2 (5 x + 2 y) \times 5 = 16 \times 5 6 x - 10 y = - 18 25 x + 10 y = 80$

Step 4. Calculation

The equation become -

$6 x - 10 y = - 18 25 x + 10 y = 80$

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

$\begin{array}{l} 6 x - 10 y = - 18 \\ \frac{25 x + 10 y = 80}{31 x = 62} \end{array}$

Solve for x -

$x = 2$

Substitute $x = 2$ into the second equation $5 x + 2 y = 16$ , Then Solve for y -

$5 x + 2 y = 16 5 \times 2 + 2 y = 16 10 + 2 y = 16 2 y = 16 - 10 2 y = 6 y = 3$

Written as $(x, y)$ will be $(2, 3)$

Step 5. Check the answer

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

Put $(2, 3)$ in the equations -

$3 x - 5 y = - 9 3 \times 2 - 5 \times 3 = - 9 6 - 15 = - 9 - 9 = - 9$

$5 x + 2 y = 16 5 \times 2 + 2 \times 3 = 16 10 + 6 = 16 16 = 16$

The Solution is - $(2, 3)$

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Solve a System of Equations by Elimination -
$3 x - 5 y = - 9 5 x + 2 y = 16$

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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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.

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Solve a System of Equations by Elimination -
$3 x - 5 y = - 9 5 x + 2 y = 16$