Symbol

# Calculator search results

Formula
Solve the system of equations
Graph
$x - y = 5$
$2 x - 3 y = 13$
$x$Intercept
$\left ( 5 , 0 \right )$
$y$Intercept
$\left ( 0 , - 5 \right )$
$x$Intercept
$\left ( \dfrac { 13 } { 2 } , 0 \right )$
$y$Intercept
$\left ( 0 , - \dfrac { 13 } { 3 } \right )$
$\begin{cases} x-y = 5 \\2x-3y = 13 \end{cases}$
$x = 2 , y = - 3$
Solve quadratic equations using the square root
$\begin{cases} x - y = 5 \\ 2 x - 3 y = 13 \end{cases}$
 Solve a solution to $x$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 5 } \\ 2 x - 3 y = 13 \end{cases}$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 5 } \\ \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ y } = \color{#FF6800}{ 13 } \end{cases}$
 Substitute the given $x$ value into the equation $2 x - 3 y = 13$
$\color{#FF6800}{ 2 } \left ( \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 5 } \right ) \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ y } = \color{#FF6800}{ 13 }$
$\color{#FF6800}{ 2 } \left ( \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 5 } \right ) \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ y } = \color{#FF6800}{ 13 }$
 Solve a solution to $y$
$\color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 3 }$
$\color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 3 }$
 Substitute the given $y$ value into the equation $x = y + 5$
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ + } \color{#FF6800}{ 5 }$
$x = \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ + } \color{#FF6800}{ 5 }$
 Add $- 3$ and $5$
$x = \color{#FF6800}{ 2 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ 2 }$
 The possible solutions are as follows 
$\color{#FF6800}{ x } = \color{#FF6800}{ 2 } , \color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 3 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ 2 } , \color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 3 }$
 Check if it is the solution to the system of equations 
$\begin{cases} \color{#FF6800}{ 2 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right ) = \color{#FF6800}{ 5 } \\ \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right ) = \color{#FF6800}{ 13 } \end{cases}$
$\begin{cases} \color{#FF6800}{ 2 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right ) = \color{#FF6800}{ 5 } \\ \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right ) = \color{#FF6800}{ 13 } \end{cases}$
 Simplify the equality 
$\begin{cases} \color{#FF6800}{ 5 } = \color{#FF6800}{ 5 } \\ \color{#FF6800}{ 13 } = \color{#FF6800}{ 13 } \end{cases}$
$\begin{cases} \color{#FF6800}{ 5 } = \color{#FF6800}{ 5 } \\ \color{#FF6800}{ 13 } = \color{#FF6800}{ 13 } \end{cases}$
 Since it is true in both equations, it is the solution of the system of equations 
$\color{#FF6800}{ x } = \color{#FF6800}{ 2 } , \color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 3 }$
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