qanda-logo
search-icon
Symbol
apple-logo
google-play-logo

Calculator search results

Formula
Solve the system of equations
Answer
circle-check-icon
expand-arrow-icon
expand-arrow-icon
expand-arrow-icon
Graph
$x + y = 12$
$10 y + x = 10 x + y + 18$
$x$Intercept
$\left ( 12 , 0 \right )$
$y$Intercept
$\left ( 0 , 12 \right )$
$x$Intercept
$\left ( - 2 , 0 \right )$
$y$Intercept
$\left ( 0 , 2 \right )$
$\begin{cases} x+y = 12 \\10y+x = 10x+y+18 \end{cases}$
$x = 5 , y = 7$
Solve quadratic equations using the square root
$\begin{cases} x + y = 12 \\ 10 y + x = 10 x + y + 18 \end{cases}$
$ $ Solve a solution to $ x$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 12 } \\ 10 y + x = 10 x + y + 18 \end{cases}$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 12 } \\ \color{#FF6800}{ 10 } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ x } = \color{#FF6800}{ 10 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 18 } \end{cases}$
$ $ Substitute the given $ x $ value into the equation $ 10 y + x = 10 x + y + 18$
$\color{#FF6800}{ 10 } \color{#FF6800}{ y } \color{#FF6800}{ + } \left ( \color{#FF6800}{ - } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 12 } \right ) = \color{#FF6800}{ 10 } \left ( \color{#FF6800}{ - } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 12 } \right ) \color{#FF6800}{ + } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 18 }$
$\color{#FF6800}{ 10 } \color{#FF6800}{ y } \color{#FF6800}{ + } \left ( \color{#FF6800}{ - } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 12 } \right ) = \color{#FF6800}{ 10 } \left ( \color{#FF6800}{ - } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 12 } \right ) \color{#FF6800}{ + } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 18 }$
$ $ Solve a solution to $ y$
$\color{#FF6800}{ y } = \color{#FF6800}{ 7 }$
$\color{#FF6800}{ y } = \color{#FF6800}{ 7 }$
$ $ Substitute the given $ y $ value into the equation $ x = - y + 12$
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 7 } \color{#FF6800}{ + } \color{#FF6800}{ 12 }$
$x = \color{#FF6800}{ - } \color{#FF6800}{ 7 } \color{#FF6800}{ + } \color{#FF6800}{ 12 }$
$ $ Add $ - 7 $ and $ 12$
$x = \color{#FF6800}{ 5 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ 5 }$
$ $ The possible solutions are as follows $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ 5 } , \color{#FF6800}{ y } = \color{#FF6800}{ 7 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ 5 } , \color{#FF6800}{ y } = \color{#FF6800}{ 7 }$
$ $ Check if it is the solution to the system of equations $ $
$\begin{cases} \color{#FF6800}{ 5 } \color{#FF6800}{ + } \color{#FF6800}{ 7 } = \color{#FF6800}{ 12 } \\ \color{#FF6800}{ 10 } \color{#FF6800}{ \times } \color{#FF6800}{ 7 } \color{#FF6800}{ + } \color{#FF6800}{ 5 } = \color{#FF6800}{ 10 } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } \color{#FF6800}{ + } \color{#FF6800}{ 7 } \color{#FF6800}{ + } \color{#FF6800}{ 18 } \end{cases}$
$\begin{cases} \color{#FF6800}{ 5 } \color{#FF6800}{ + } \color{#FF6800}{ 7 } = \color{#FF6800}{ 12 } \\ \color{#FF6800}{ 10 } \color{#FF6800}{ \times } \color{#FF6800}{ 7 } \color{#FF6800}{ + } \color{#FF6800}{ 5 } = \color{#FF6800}{ 10 } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } \color{#FF6800}{ + } \color{#FF6800}{ 7 } \color{#FF6800}{ + } \color{#FF6800}{ 18 } \end{cases}$
$ $ Simplify the equality $ $
$\begin{cases} \color{#FF6800}{ 12 } = \color{#FF6800}{ 12 } \\ \color{#FF6800}{ 75 } = \color{#FF6800}{ 75 } \end{cases}$
$\begin{cases} \color{#FF6800}{ 12 } = \color{#FF6800}{ 12 } \\ \color{#FF6800}{ 75 } = \color{#FF6800}{ 75 } \end{cases}$
$ $ Since it is true in both equations, it is the solution of the system of equations $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ 5 } , \color{#FF6800}{ y } = \color{#FF6800}{ 7 }$
Have you found the solution you wanted?
Try again
Try more features at Qanda!
Search by problem image
Ask 1:1 question to TOP class teachers
AI recommend problems and video lecture
apple-logo
google-play-logo