Chapter 5: Q 90. (page 611)

Solve the system of equation $\{\begin{cases} 4 x + y = 10 \\ x - 2 y = - 20 \end{cases}$ by substitution

Short Answer

Expert verified

The solution is $(0, 10)$ .

Step by step solution

Step 1. Given information

The given equations are:

$4 x + y = 10 \dots \dots (1)$

$x - 2 y = - 20 \dots \dots (2)$

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

From equation $(1)$ , $y = 10 - 4 x$

Put in equation $(2)$

$\Rightarrow x - 2 (10 - 4 x) = - 20$

Step 3. Solve for x

$\Rightarrow x - 20 + 8 x = - 20$

$\Rightarrow 9 x = - 20 + 20$

$\Rightarrow 9 x = 0$

$\Rightarrow x = 0$

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

$\Rightarrow 0 - 2 y = - 20$

$\Rightarrow y = \frac{- 20}{- 2}$

$\Rightarrow y = 10$

Step 5. Checking solution

Now we have $x = 0$ and $y = 10$

Put these values in equation $(1)$

$\Rightarrow 4 (0) + 10 = 10$

$\Rightarrow 10 = 10$

Also put these values in equation $(2)$

$\Rightarrow 0 - 2 (10) = - 20$

$\Rightarrow - 20 = - 20$

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Solve the system of equation $\{\begin{cases} 4 x + y = 10 \\ x - 2 y = - 20 \end{cases}$ 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 equation4x+y=10x-2y=-20by 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

Probability and Statistics

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Statistics

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Theoretical and Mathematical Physics

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Study anywhere. Anytime. Across all devices.

Solve the system of equation $\{\begin{cases} 4 x + y = 10 \\ x - 2 y = - 20 \end{cases}$ by substitution