Chapter 5: Q 78. (page 611)

Solve the system of equation $\{\begin{cases} 2 x + 5 y = - 14 \\ y = - 2 x + 2 \end{cases}$ by substitution

Short Answer

Expert verified

The solution is $(3, - 4)$ .

Step by step solution

Step 1. Given information

The given equations are:

$2 x + 5 y = - 14 \dots \dots (1)$

$y = - 2 x + 2 \dots \dots (2)$

Step 2. Substitute value of y from equation 2 in equation 1

$\Rightarrow 2 x + 5 (- 2 x + 2) = - 14$

Step 3. Solve for x

$\Rightarrow 2 x - 10 x + 10 = - 14$

$\Rightarrow - 8 x = - 14 - 10$

$\Rightarrow - 8 x = - 24$

$\Rightarrow x = 3$

Step 4. Substitute value of x from step 3 in equation 2

$\Rightarrow y = - 2 (3) + 2$

$\Rightarrow y = - 6 + 2$

$\Rightarrow y = - 4$

Step 5. Checking solution

Now we have $x = 3$ and $y = - 4$

Put these values in equation $(1)$

$\Rightarrow 2 (3) + 5 (- 4) = - 14$

$\Rightarrow - 14 = - 14$

Also put these values in equation $(2)$

$\Rightarrow - 4 = - 2 (3) + 2$

$\Rightarrow - 4 = - 4$

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Solve the system of equation $\{\begin{cases} 2 x + 5 y = - 14 \\ y = - 2 x + 2 \end{cases}$ by substitution

Short Answer

Step by step solution

Step 1. Given information

Step 2. Substitute value of y from equation 2 in equation 1

Step 3. Solve for x

Step 4. Substitute value of x from step 3 in equation 2

Step 5. Checking solution

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Solve the system of equation 2x+5y=-14y=-2x+2by substitution

Short Answer

Step by step solution

Step 1. Given information

Step 2. Substitute value of y from equation 2 in equation 1

Step 3. Solve for x

Step 4. Substitute value of x from step 3 in equation 2

Step 5. Checking solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

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Study anywhere. Anytime. Across all devices.

Solve the system of equation $\{\begin{cases} 2 x + 5 y = - 14 \\ y = - 2 x + 2 \end{cases}$ by substitution