Algebra I HON HW-Applications of Systems of Linear Equations (1) The sum of two numbers is 125 and their difference is 47. Find each of the numbers. (2) The first number is 5 more than the second number is 2 less than 3 times the second number. Find the numbers. (3)The sum of 6 times JennIfer's age and 5 times James' age is 150. James is 2 years less than twice as old as Jennifer is.Find each of their ages. (4) The perimeter of a rectangle is 44 cm.. The length is 2 cm more than three times the width. Find the dimensions of the rectangle. (5))The perimeter of a rectangle is 122 m.The length of the rectangle is 11 mless than five times the width. Find the dimensions of the rectangle.

## Step 1:<br />For the first problem, we are given two equations: \(x + y = 125\) and \(x - y = 47\). We can solve this system of equations by adding the two equations together.<br /><br />## Step 2:<br />For the second problem, we are given two equations: \(x = y + 5\) and \(2x = 3y - 2\). We can substitute the first equation into the second one to solve for \(y\), and then substitute \(y\) back into the first equation to solve for \(x\).<br /><br />## Step 3:<br />For the third problem, we are given two equations: \(6x + 5y = 150\) and \(y = 2x - 2\). We can substitute the second equation into the first one to solve for \(x\), and then substitute \(x\) back into the second equation to solve for \(y\).<br /><br />## Step 4:<br />For the fourth problem, we are given two equations: \(2x + 2y = 44\) and \(x = 3y + 2\). We can substitute the second equation into the first one to solve for \(y\), and then substitute \(y\) back into the second equation to solve for \(x\).<br /><br />## Step 5:<br />For the fifth problem, we are given two equations: \(2x + 2y = 122\) and \(x = 5y - 11\). We can substitute the second equation into the first one to solve for \(y\), and then substitute \(y\) back into the second equation to solve for \(x\).