Question

What value does "h" have in this equation for this to be an infinite solutions equation. 6 (hx + 5) + 4 = -4(8 - 4(8 – 18x) 18x) + 66

Answer 1

We have the following:

$6(hx+5)+4=-4(8-18x)+66$

A system of linear equations has infinite solutions when the graphs are exactly the same line.

for this to happen, on both sides the value of x must be equal:

$\begin{gathered} 6\cdot h=4\cdot18 \\ h=4\cdot\frac{18}{6} \\ h=12 \end{gathered}$

replacing:

$\begin{gathered} 6\cdot(12x+5)+4=-4\cdot(8-18x)+66 \\ 72x+30+4=-32+72x+66 \\ 7x+34=7x+34 \\ 0=0 \\ \text{true for all x} \end{gathered}$