Question

solving systems of linear equations: substitution
cassandra is comparing two different subscription plans for a streaming service. the plans have a promotional decreasing
cost. the basic plan starts at $18 for the first month and decreases by $1 for each subsequent month, represented by the
equation ( y = 18 - x ). the premium plan costs 1.25 times the monthly cost of the basic plan, which is represented by the
equation ( x = 1.25 y ). after how many months will the costs of both plans be equal?
enter your answer in the box.

Explanation:

Step1: Substitute the first equation into the second

Given \(y = 18 - x\) and \(x=1.25y\). Substitute \(y\) in the second equation: \(x = 1.25(18 - x)\).

Step2: Expand the right - hand side

Using the distributive property \(a(b - c)=ab - ac\), we have \(x=1.25\times18-1.25x\). So \(x = 22.5-1.25x\).

Step3: Add \(1.25x\) to both sides

\(x + 1.25x=22.5-1.25x+1.25x\). Combining like terms, \((1 + 1.25)x=22.5\), i.e., \(2.25x = 22.5\).

Step4: Solve for \(x\)

Divide both sides by \(2.25\): \(x=\frac{22.5}{2.25}\). Since \(22.5\div2.25 = 10\).

Answer:

\(10\)