Chapter 4: Q. 339 (page 479)

In the following exercises, solve the systems of equations by substitution.
$\{\begin{cases} y = - 2 x + 7 \\ y = \frac{2}{3} x - 1 \end{cases}$

Short Answer

Expert verified

The solution for the system of linear equations is $(3, 1)$ .

Step by step solution

Step 1. Given information.

The system of linear equations,

$\{\begin{cases} y = - 2 x + 7 \\ y = \frac{2}{3} x - 1 \end{cases}$

Step 2. Substituting the value of y from one equation into another equation.

$y = - 2 x + 7$
Now substituting this in another equation we get

$- 2 x + 7 = \frac{2}{3} x - 1 - 2 x + 8 = \frac{2}{3} x - 6 x + 24 = 2 x 8 x = 24 x = 3$

Step 3. Substituting the value of x in any equation.

$y = - 2 (3) + 7 y = - 6 + 7 y = 1$

Step 4. Checking the result.

Substituting the value of $x$ and $y$ in the first equation then

$y = - 2 x + 7 1 = - 2 (3) + 7 1 = - 6 + 7 1 = 1$

Substituting the value of $x$ and $y$ in the second equation then

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

Hence, this is true.

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In the following exercises, solve the systems of equations by substitution.
$\{\begin{cases} y = - 2 x + 7 \\ y = \frac{2}{3} x - 1 \end{cases}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Substituting the value of y from one equation into another equation.

Step 3. Substituting the value of x in any equation.

Step 4. Checking the result.

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In the following exercises, solve the systems of equations by substitution.y=-2x+7y=23x-1

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Substituting the value of y from one equation into another equation.

Step 3. Substituting the value of x in any equation.

Step 4. Checking the result.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Statistics

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Study anywhere. Anytime. Across all devices.

In the following exercises, solve the systems of equations by substitution.
$\{\begin{cases} y = - 2 x + 7 \\ y = \frac{2}{3} x - 1 \end{cases}$