Chapter 5: Q 91. (page 611)

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

Short Answer

Expert verified

The solution is $(- 3, 5)$ .

Step by step solution

Step 1. Given information

The given equations are:

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

$y = - \frac{1}{3} x + 4 \dots \dots (2)$

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

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

Step 3. Solve for x

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

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

$\Rightarrow \frac{- 5 x}{3} = 5$

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

$\Rightarrow x = - 3$

Step 4. Substitute value of x from step 3 in equation 1

$\Rightarrow y = - 2 (- 3) - 1$

$\Rightarrow y = 6 - 1$

$\Rightarrow y = 5$

Step 5. Checking solution

Now we have $x = - 3$ and $y = 5$

Put these values in equation $(1)$

$\Rightarrow 5 = - 2 (- 3) - 1$

$\Rightarrow 5 = 5$

Also put these values in equation $(2)$

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

$\Rightarrow 5 = 5$

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

Step 5. Checking solution

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Solve the system of equationy=-2x-1y=-13x+4by 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 1

Step 5. Checking solution

One App. One Place for Learning.

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