Chapter 5: Q 88. (page 611)

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

Short Answer

Expert verified

The solution is $(5, - 3)$

Step by step solution

Step 1. Given information

The given equations are:

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

$2 x + 3 y = 1 \dots \dots (2)$

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

From equation $(1)$ , $x = - 1 - 2 y$

Put in equation $(2)$

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

Step 3. Solve for y

$\Rightarrow - 2 - 4 y + 3 y = 1$

$\Rightarrow - y = 1 + 2$

$\Rightarrow - y = 3$

$\Rightarrow y = - 3$

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

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

$\Rightarrow x - 6 = - 1$

$\Rightarrow x = - 1 + 6$

$\Rightarrow x = 5$

Step 5. Checking solution

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

Put these values in equation $(1)$

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

$\Rightarrow - 1 = - 1$

Also put these values in equation $(2)$

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

$\Rightarrow 1 = 1$

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Solve the system of equation $\{\begin{cases} x + 2 y = - 1 \\ 2 x + 3 y = 1 \end{cases}$ 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+2y=-12x+3y=1by 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.

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