Chapter 5: Q 80. (page 611)

Solve the system of equation $\{\begin{cases} 3 x + 4 y = 1 \\ y = - \frac{2}{5} x + 2 \end{cases}$ by substitution

Short Answer

Expert verified

The solution is $(- 5, 4)$ .

Step by step solution

Step 1. Given information

The given equations are:

$3 x + 4 y = 1 \dots \dots (1)$

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

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

$\Rightarrow 3 x + 4 (- \frac{2}{5} x + 2) = 1$

Step 3. Solve for x

$\Rightarrow 3 x - \frac{8}{5} x + 8 = 1$

$\Rightarrow \frac{15 x - 8 x}{5} = 1 - 8$

$\Rightarrow \frac{7 x}{5} = - 7$

" width="9" height="19" role="math">⇒7x=-35

$\Rightarrow x = - \frac{35}{7}$

$\Rightarrow x = - 5$

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

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

$\Rightarrow y = 2 + 2$

$\Rightarrow y = 4$

Step 5. Checking solution

Now we have $x = - 5$ and $y = 4$

Put these values in equation $(1)$

$\Rightarrow 3 (- 5) + 4 (4) = 1$

$\Rightarrow 1 = 1$

Also put these values in equation $(2)$

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

$\Rightarrow 4 = 4$

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Solve the system of equation $\{\begin{cases} 3 x + 4 y = 1 \\ y = - \frac{2}{5} x + 2 \end{cases}$ 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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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

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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 $\{\begin{cases} 3 x + 4 y = 1 \\ y = - \frac{2}{5} x + 2 \end{cases}$ by substitution