Chapter 5: Q 79. (page 611)

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

Short Answer

Expert verified

The solution is $(3, - 1)$ .

Step by step solution

Step 1. Given information

The given equations are:

$2 x + 5 y = 1 \dots \dots (1)$

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

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

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

Step 3. Solve for x

$\Rightarrow 2 x + \frac{5}{3} x - 10 = 1$

$\Rightarrow \frac{6 x + 5 x}{3} = 1 + 10$

$\Rightarrow \frac{11}{3} x = 11$

$\Rightarrow x = \frac{33}{11}$

$\Rightarrow x = 3$

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

$\Rightarrow y = \frac{1}{3} (3) - 2$

$\Rightarrow y = 1 - 2$

$\Rightarrow y = - 1$

Step 5. Checking solution

Now we have $x = 3$ and $y = - 1$

Put these values in equation $(1)$

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

$\Rightarrow 1 = 1$

Also put these values in equation $(2)$

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

$\Rightarrow - 1 = - 1$

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

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Step 5. Checking solution

One App. One Place for Learning.

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