Chapter 5: Q 87. (page 611)

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

Short Answer

Expert verified

The solution is $(- 5, 2)$ .

Step by step solution

Step 1. Given information

The given equations are:

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

$3 x + 5 y = - 5 \dots \dots (2)$

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

From equation $(1)$ , $x = 1 - 3 y$

Put in equation $(2)$

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

Step 3. Solve for y

$\Rightarrow 3 - 9 y + 5 y = - 5$

$\Rightarrow - 4 y = - 5 - 3$

$\Rightarrow - 4 y = - 8$

$\Rightarrow y = \frac{- 8}{- 4}$

$\Rightarrow y = 2$

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

$\Rightarrow x + 3 (2) = 1$

$\Rightarrow x + 6 = 1$

$\Rightarrow x = 1 - 6$

$\Rightarrow x = - 5$

Step 5. Checking solution

Now we have $x = - 5$ and $y = 2$

Put these values in equation $(1)$

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

$\Rightarrow 1 = 1$

Also put these values in equation $(2)$

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

$\Rightarrow - 5 = - 5$

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

Short Answer

Step by step solution

Step 1. Given information

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

Step 3. Solve for y

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

Step 5. Checking solution

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Solve the system of equationx+3y=13x+5y=-5by substitution

Short Answer

Step by step solution

Step 1. Given information

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

Step 3. Solve for y

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

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