Question

Solve each system by graphing. Tell whether the system has one solution, infinitely many solutions, or no solution.

2x2y=5y=x4\left. \begin{array} { l } { 2 x - 2 y = 5 } \\ { y = x - 4 } \end{array} \right.

Solution

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2x2y=52x-2y=5

y=x4y=x-4

$\text{\textcolor{#4257b2}{Substitute the value of y\color{#c34632}y into the equation\ 2x2y=5\color{#c34632}2x-2y=5}}$

2x2(x4)=52x-2(x-4)=5

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

2x2x+8=52x-2x+8=5

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

8=58=5

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

xϕ\color{#c34632}\boxed{x \in \phi}

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