qanda-logo
search-icon
Symbol

Calculator search results

Solve the system of equations
Answer
circle-check-icon
expand-arrow-icon
expand-arrow-icon
Graph
$5 x + 3 y = 17$
$x = y - 3$
$x$Intercept
$\left ( \dfrac { 17 } { 5 } , 0 \right )$
$y$Intercept
$\left ( 0 , \dfrac { 17 } { 3 } \right )$
$x$Intercept
$\left ( - 3 , 0 \right )$
$y$Intercept
$\left ( 0 , 3 \right )$
$x = 1 , y = 4$
Solve the system of equations
$\begin{cases} \color{#FF6800}{ 5 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \color{#FF6800}{ y } = \color{#FF6800}{ 17 } \\ \color{#FF6800}{ x } = \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \end{cases}$
$ $ Substitute the given $ x $ value into the equation $ 5 x + 3 y = 17$
$\color{#FF6800}{ 5 } \left ( \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 3 } \color{#FF6800}{ y } = \color{#FF6800}{ 17 }$
$\color{#FF6800}{ 5 } \left ( \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 3 } \color{#FF6800}{ y } = \color{#FF6800}{ 17 }$
$ $ Solve a solution to $ y$
$\color{#FF6800}{ y } = \color{#FF6800}{ 4 }$
$\color{#FF6800}{ y } = \color{#FF6800}{ 4 }$
$ $ Substitute the given $ y $ value into the equation $ x = y - 3$
$\color{#FF6800}{ x } = \color{#FF6800}{ 4 } \color{#FF6800}{ - } \color{#FF6800}{ 3 }$
$x = \color{#FF6800}{ 4 } \color{#FF6800}{ - } \color{#FF6800}{ 3 }$
$ $ Subtract $ 3 $ from $ 4$
$x = \color{#FF6800}{ 1 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ 1 }$
$ $ The possible solutions are as follows $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ 1 } , \color{#FF6800}{ y } = \color{#FF6800}{ 4 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ 1 } , \color{#FF6800}{ y } = \color{#FF6800}{ 4 }$
$ $ Check if it is the solution to the system of equations $ $
$\begin{cases} \color{#FF6800}{ 5 } \color{#FF6800}{ \times } \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 4 } = \color{#FF6800}{ 17 } \\ \color{#FF6800}{ 1 } = \color{#FF6800}{ 4 } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \end{cases}$
$\begin{cases} \color{#FF6800}{ 5 } \color{#FF6800}{ \times } \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 4 } = \color{#FF6800}{ 17 } \\ \color{#FF6800}{ 1 } = \color{#FF6800}{ 4 } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \end{cases}$
$ $ Simplify the equality $ $
$\begin{cases} \color{#FF6800}{ 17 } = \color{#FF6800}{ 17 } \\ \color{#FF6800}{ 1 } = \color{#FF6800}{ 1 } \end{cases}$
$\begin{cases} \color{#FF6800}{ 17 } = \color{#FF6800}{ 17 } \\ \color{#FF6800}{ 1 } = \color{#FF6800}{ 1 } \end{cases}$
$ $ Since it is true in both equations, it is the solution of the system of equations $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ 1 } , \color{#FF6800}{ y } = \color{#FF6800}{ 4 }$
Have you found the solution you wanted?
Try again
Try more features at Qanda!
check-iconSearch by problem image
check-iconAsk 1:1 question to TOP class teachers
check-iconAI recommend problems and video lecture