Chapter 5: Q 89. (page 611)

Solve the system of equation $\{\begin{cases} 2 x + y = 5 \\ x - 2 y = - 15 \end{cases}$ by substitution

Short Answer

Expert verified

The solution is $(- 1, 7)$

Step by step solution

Step 1. Given information

The given equations are:

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

$x - 2 y = - 15 \dots \dots (2)$

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

From equation $(1)$ , $y = 5 - 2 x$

Put in equation $(2)$

$\Rightarrow x - 2 (5 - 2 x) = - 15$

Step 3. Solve for x

$\Rightarrow x - 10 + 4 x = - 15$

$\Rightarrow 5 x = - 15 + 10$

$\Rightarrow 5 x = - 5$

$\Rightarrow x = \frac{- 5}{5}$

$\Rightarrow x = - 1$

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

$\Rightarrow - 1 - 2 y = - 15$

$\Rightarrow - 2 y = - 14$

$\Rightarrow y = \frac{- 14}{- 2}$

$\Rightarrow y = 7$

Step 5. Checking solution

Now we have $x = - 1$ and $y = 7$

Put these values in equation $(1)$

$\Rightarrow 2 (- 1) + 7 = 5$

$\Rightarrow 5 = 5$

Also put these values in equation $(7)$

$\Rightarrow - 1 - 2 (7) = - 15$

$\Rightarrow - 15 = - 15$

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Solve the system of equation $\{\begin{cases} 2 x + y = 5 \\ x - 2 y = - 15 \end{cases}$ by substitution

Short Answer

Step by step solution

Step 1. Given information

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

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 equation2x+y=5x-2y=-15by substitution

Short Answer

Step by step solution

Step 1. Given information

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

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

Statistics

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Study anywhere. Anytime. Across all devices.

Solve the system of equation $\{\begin{cases} 2 x + y = 5 \\ x - 2 y = - 15 \end{cases}$ by substitution