Chapter 5: Q 84. (page 611)

Solve the system of equation $\{\begin{cases} - 2 x + y = 10 \\ - x + 2 y = 16 \end{cases}$ by substitution

Short Answer

Expert verified

The solution is $(- \frac{4}{3}, \frac{22}{3})$ .

Step by step solution

Step 1. Given information

The given equations are:

$- 2 x + y = 10 \dots \dots (1)$

$- x + 2 y = 16 \dots \dots (2)$

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

From equation $(1)$ , $y = 10 + 2 x$

Put in equation $(2)$

$\Rightarrow - x + 2 (10 + 2 x) = 16$

Step 3. Solve for x

$\Rightarrow - x + 20 + 4 x = 16$

$\Rightarrow 3 x = 16 - 20$

$\Rightarrow 3 x = - 4$

$\Rightarrow x = - \frac{4}{3}$

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

$\Rightarrow - (- \frac{4}{3}) + 2 y = 16$

$\Rightarrow 2 y = 16 - \frac{4}{3}$

$\Rightarrow 2 y = \frac{48 - 4}{3}$

$\Rightarrow 2 y = \frac{44}{3}$

$\Rightarrow y = \frac{22}{3}$

Step 5. Checking solution

Now we have $x = - \frac{4}{3}$ and $y = \frac{22}{3}$

Put these values in equation $(1)$

$\Rightarrow - 2 (- \frac{4}{3}) + \frac{22}{3} = 10$

$\Rightarrow 10 = 10$

Also put these values in equation $(2)$

$\Rightarrow - (- \frac{4}{3}) + 2 (\frac{22}{3}) = 16$

$\Rightarrow 16 = 16$

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Solve the system of equation $\{\begin{cases} - 2 x + y = 10 \\ - x + 2 y = 16 \end{cases}$ 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 equation-2x+y=10-x+2y=16by 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

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Solve the system of equation $\{\begin{cases} - 2 x + y = 10 \\ - x + 2 y = 16 \end{cases}$ by substitution