Chapter 5: Q 82. (page 611)

Solve the system of equation $\{\begin{cases} - 3 x - 5 y = 3 \\ y = \frac{1}{2} x - 5 \end{cases}$ by substitution

Short Answer

Expert verified

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

Step by step solution

Step 1. Given information

The given equations are:

$- 3 x - 5 y = 3 \dots \dots (1)$

$y = \frac{1}{2} x - 5 \dots \dots (2)$

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

$- 3 x - 5 (\frac{1}{2} x - 5) = 3$

Step 3. Solve for x

$\Rightarrow - 3 x - \frac{5}{2} x + 25 = 3$

$\Rightarrow \frac{- 6 x - 5 x}{2} = 3 - 25$

$\Rightarrow - \frac{11}{2} x = - 22$

$\Rightarrow x = \frac{- 44}{- 11}$

$\Rightarrow x = 4$

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

$\Rightarrow y = \frac{1}{2} (4) - 5$

$\Rightarrow y = 2 - 5$

$\Rightarrow y = - 3$

Step 5. Checking solution

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

Put these values in equation $(1)$

$\Rightarrow - 3 (4) - 5 (- 3) = 3$

$\Rightarrow 3 = 3$

Also put these values in equation $(2)$

role="math" localid="1649087818803" $\Rightarrow - 3 = \frac{1}{2} (4) - 5$

role="math" localid="1649087837741" $\Rightarrow - 3 = - 3$

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Solve the system of equation $\{\begin{cases} - 3 x - 5 y = 3 \\ y = \frac{1}{2} x - 5 \end{cases}$ 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-3x-5y=3y=12x-5by 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

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Study anywhere. Anytime. Across all devices.

Solve the system of equation $\{\begin{cases} - 3 x - 5 y = 3 \\ y = \frac{1}{2} x - 5 \end{cases}$ by substitution