Question

# Solve each system by graphing. Tell whether the system has one solution, infinitely many solutions, or no solution.$\left. \begin{array} { l } { 2 x - 2 y = 5 } \\ { y = x - 4 } \end{array} \right.$

Solution

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Step 1
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$2x-2y=5$

$y=x-4$

$\text{\textcolor{#4257b2}{Substitute the value of $\color{#c34632}y$ into the equation\ $\color{#c34632}2x-2y=5$}}$

$2x-2(x-4)=5$

$\text{\textcolor{#4257b2}{Distribute (-2) through the parenthesis}}$

$2x-2x+8=5$

$\text{\textcolor{#4257b2}{Eliminate the opposites}}$

$8=5$

$\text{\textcolor{#c34632}{The statement is false for any value of $x$}}$

$\color{#c34632}\boxed{x \in \phi}$

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