Chapter 5: Q 77. (page 611)

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

Short Answer

Expert verified

The solution is $(6, - 3)$ .

Step by step solution

Step 1. Given information

The given equations are:

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

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

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

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

Step 3. Solve for x

$\Rightarrow 2 x - 3 x + 9 = 3$

$\Rightarrow - x = 3 - 9$

$\Rightarrow - x = - 6$

$\Rightarrow x = 6$

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

$\Rightarrow y = - 6 + 3$

$\Rightarrow y = - 3$

Step 5. Checking solution

Now we have $x = 6$ and $y = - 3$

Put these values in equation $(1)$

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

$\Rightarrow 3 = 3$

Also put these values in equation $(2)$

$\Rightarrow - 3 = - 6 + 3$

$\Rightarrow - 3 = - 3$

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Solve the system of equation $\{\begin{cases} 2 x + 3 y = 3 \\ y = - x + 3 \end{cases}$ 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 equation2x+3y=3y=-x+3 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

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Logic and Functions

Decision Maths

Discrete Mathematics

Calculus

Geometry

Study anywhere. Anytime. Across all devices.

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