Question

# Identify the segment bisector of 𝑃𝑅 and find 𝑃𝑄.

Hint:

### Line which bisects the line segment in two equal parts is called segment bisector.

## The correct answer is: 8 units.

- Step-by-step explanation:

○ Given:

PQ = 5y - 7

QR = y + 5

○ Step 1:

As we know, the segment bisector divides the line segment in two equal parts.

So,

As Q is midpoint of PR

∴ PQ = QR

5y - 7 = y + 5

5y - y = 7 + 5

4y = 12

y =

y = 3

○ Step 2:

○ Put y = 3 in 5y - 7 we will get PQ.

PQ = 5y -7

PQ = 5(3) - 7

PQ = 15 - 7

PQ = 8 units.

- Final Answer:

Hence, line l is segment bisector of PR and PQ = 8 units.

○ Step 1:

As we know, the segment bisector divides the line segment in two equal parts.

So,

As Q is midpoint of PR

∴ PQ = QR

○ Step 2:

○ Put y = 3 in 5y - 7 we will get PQ.

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Finding the answer to the given linear equation is the act of solving a linear equation. One of the algebraic techniques for solving a system of two-variable linear equations is the substitution approach. As the name suggests, the replacement method involves substituting a variable's value into a second equation. As a result, two linear equations are combined into one linear equation with just one variable, making it simple to solve. As an illustration, let us swap the value of the x-variable from the second equation and the y-variable from the first equation. By solving the problem, we can determine the value of the y-variable. Last but not least, we can solve any of the preceding equations by substituting the value of y. This procedure can easily be switched around so that we first solve for x before moving on to solve for y.

### Use Substitution to solve each system of equations :

Y = 2X - 7

9X + Y = 15

Finding the answer to the given linear equation is the act of solving a linear equation. One of the algebraic techniques for solving a system of two-variable linear equations is the substitution approach. As the name suggests, the replacement method involves substituting a variable's value into a second equation. As a result, two linear equations are combined into one linear equation with just one variable, making it simple to solve. As an illustration, let us swap the value of the x-variable from the second equation and the y-variable from the first equation. By solving the problem, we can determine the value of the y-variable. Last but not least, we can solve any of the preceding equations by substituting the value of y. This procedure can easily be switched around so that we first solve for x before moving on to solve for y.