Chapter 5: Q 81. (page 611)

Solve the system of equation $\{\begin{cases} 3 x - 2 y = 6 \\ y = \frac{2}{3} x + 2 \end{cases}$ by substitution

Short Answer

Expert verified

The solution is $(6, 6)$ .

Step by step solution

Step 1. Given information

The given equations are:

$3 x - 2 y = 6 \dots \dots (1)$

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

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

$\Rightarrow 3 x - 2 (\frac{2}{3} x + 2) = 6$

Step 3. Solve for x

$\Rightarrow 3 x - \frac{4}{3} x - 4 = 6$

$\Rightarrow \frac{9 x - 4 x}{3} = 6 + 4$

$\Rightarrow \frac{5}{3} x = 10$

$\Rightarrow 5 x = 30$

$\Rightarrow x = 6$

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

$\Rightarrow y = \frac{2}{3} (6) + 2$

$\Rightarrow y = 4 + 2$

$\Rightarrow y = 6$

Step 5. Checking solution

Now we have $x = 6$ and $y = 6$

Put these values in equation $(1)$

$\Rightarrow 3 (6) - 2 (6) = 6$

$\Rightarrow 6 = 6$

Also put these values in equation $(2)$

$\Rightarrow 6 = \frac{2}{3} (6) + 2$

$\Rightarrow 6 = 6$

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Solve the system of equation $\{\begin{cases} 3 x - 2 y = 6 \\ y = \frac{2}{3} x + 2 \end{cases}$ 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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Solve the system of equation3x-2y=6y=23x+2by 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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Solve the system of equation $\{\begin{cases} 3 x - 2 y = 6 \\ y = \frac{2}{3} x + 2 \end{cases}$ by substitution