Solve the system of equations 2x-y=1; x+2y=8 graphically and find the coordinates of the points where corresponding lines intersect y-axis.
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$y = 10 - 2 x$
$y = 14$
$x$Intercept
$\left ( 5 , 0 \right )$
$y$Intercept
$\left ( 0 , 10 \right )$
$x = - 2$
$ $ Solve a solution to $ x$
$\color{#FF6800}{ 10 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } = 14$
$ $ Organize the expression $ $
$\color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 10 } = 14$
$- 2 x \color{#FF6800}{ + } \color{#FF6800}{ 10 } = 14$
$ $ Move the constant to the right side and change the sign $ $
$- 2 x = 14 \color{#FF6800}{ - } \color{#FF6800}{ 10 }$
$- 2 x = \color{#FF6800}{ 14 } \color{#FF6800}{ - } \color{#FF6800}{ 10 }$
$ $ Subtract $ 10 $ from $ 14$
$- 2 x = \color{#FF6800}{ 4 }$
$\color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } = \color{#FF6800}{ 4 }$
$ $ Change the sign of both sides of the equation $ $
$2 x = - 4$
$\color{#FF6800}{ 2 } \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 4 }$
$ $ Divide both sides by the same number $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 2 }$
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1. $2x+3\times 10^{-2x}=250$ $5$
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