Question

which value, when placed in the box, would result in a system of equations with infinitely many solutions? y = 2x - 5 2y - 4x = □ -10 -5 5 10

Explanation:

Step1: Rewrite the first - equation in slope - intercept form.

Given \(y = 2x-5\) and \(2y-4x=\square\). Rewrite \(2y - 4x=\square\) as \(y=2x+\frac{\square}{2}\).
For a system of linear equations \(y = m_1x + b_1\) and \(y=m_2x + b_2\) to have infinitely many solutions, \(m_1 = m_2\) and \(b_1 = b_2\). Here \(m_1 = 2\) (from \(y = 2x-5\)) and \(m_2 = 2\) (from \(y=2x+\frac{\square}{2}\)). We need to find the value of \(\square\) such that the two equations are the same.

Step2: Set the constant terms equal.

We know that \(- 5=\frac{\square}{2}\). Cross - multiply to solve for \(\square\). Multiply both sides of the equation \(-5=\frac{\square}{2}\) by \(2\). So \(\square=-10\).

Answer:

\(-10\)