Chapter 10: Q.27 (page 546)

Solve the linear system by graphing.
$\begin{array}{l} x + y = 6 \\ 2 x - 8 y = - 11 \end{array}$

Short Answer

Expert verified

Solution of the given system is $(3.7, 2.3)$ .

Step by step solution

Step 1. Given Information.

Linear system is:

$\begin{array}{l} x + y = 6 \\ 2 x - 8 y = - 11 \end{array}$

Step 2. Property used.

Substitution property.

Step 3. Calculation.

For equation: $x + y = 6$

Put the value of x in y, Hence,

For equation: $2 x - 8 y = - 11$

Put the value of x in y, Hence,

Now, both lines meet at point $(3.7, 2.3)$ .

Equation 1: $x + y = 6$

Equation 2: $2 x - 8 y = - 11$

By substituting the value of y from equation 1 to equation 2.

$\begin{matrix} 2 x - 8 (6 - x) = - 11 \\ 2 x - 48 + 8 x = - 11 \\ 10 x = - 11 + 48 \\ x = \frac{37}{10} \end{matrix}$

Now substituting the value of x in equation 1.

$\begin{matrix} \frac{37}{10} + y = 6 \\ y = 6 - \frac{37}{10} \\ = \frac{23}{10} \end{matrix}$

Hence, both lines meet at point $(3.7, 2.3)$ .

Step 4. Conclusion.

The solution to the given linear system is $(3.7, 2.3)$ .

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Solve the linear system by graphing.
$\begin{array}{l} x + y = 6 \\ 2 x - 8 y = - 11 \end{array}$

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Property used.

Step 3. Calculation.

Step 4. Conclusion.

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Solve the linear system by graphing.x+y=62x−8y=−11

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Property used.

Step 3. Calculation.

Step 4. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

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Solve the linear system by graphing.
$\begin{array}{l} x + y = 6 \\ 2 x - 8 y = - 11 \end{array}$