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The lines $ℓ_{1}$ and $ℓ_{2}$ have equations

\begin{aligned} a x + 2 y + 4 & = 0 \\ 5 x - b y & = 0 \end{aligned}

You are given that $ℓ_{1}$ passes through $(1, - 1)$ and that $ℓ_{1}$ is parallel to $ℓ_{2} .$

Find the values of $a$ and $b .$

The point $(1, - 1)$ lies on $ℓ_{1}$ , so it satisfies its equation.

To find the gradient of a line, put its equation in the form

y = m x + c