Chapter 4: Q. 338 (page 479)

In the following exercises, solve the systems of equations by substitution.
$\{\begin{cases} x - y = 0 \\ 2 x + 5 y = - 14 \end{cases}$

Short Answer

Expert verified

The solution for the system of linear equations is $(- 2, - 2)$ .

Step by step solution

Step 1. Given information.

The system of linear equations,

$\{\begin{cases} x - y = 0 \\ 2 x + 5 y = - 14 \end{cases}$

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

$x - y = 0 y = x$

Now substituting this in another equation we get

$2 x + 5 x = - 14 7 x = - 14 x = - 2$

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

$2 (- 2) + 5 y = - 14 - 4 + 5 y = - 14 5 y = - 10 y = - 2$

Step 4. Checking the result.

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

$x - y = 0 - 2 - (- 2) = 0 - 2 + 2 = 0 0 = 0$

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

$2 x + 5 y = - 14 2 (- 2) + 5 (- 2) = - 14 - 4 - 10 = - 14 - 14 = - 14$

Hence, this is true.

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In the following exercises, solve the systems of equations by substitution.
$\{\begin{cases} x - y = 0 \\ 2 x + 5 y = - 14 \end{cases}$

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.x-y=02x+5y=-14

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

Calculus

Logic and Functions

Theoretical and Mathematical Physics

Mechanics Maths

Applied Mathematics

Pure Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, solve the systems of equations by substitution.
$\{\begin{cases} x - y = 0 \\ 2 x + 5 y = - 14 \end{cases}$