Calculator search results

Formula

Solve the system of equations

Answer

Graph

$3 x - 4 y = 4$

$- 2 x + 3 y = - 2$

$x$Intercept

$\left ( \dfrac { 4 } { 3 } , 0 \right )$

$y$Intercept

$\left ( 0 , - 1 \right )$

$x$Intercept

$\left ( 1 , 0 \right )$

$y$Intercept

$\left ( 0 , - \dfrac { 2 } { 3 } \right )$

$\begin{cases} 3x-4y = 4 \\-2x+3y = -2 \end{cases}$

$x = 4 , y = 2$

Solve the system of equations

$\begin{cases} 3 x - 4 y = 4 \\ - 2 x + 3 y = - 2 \end{cases}$

$ $ Solve a solution to $ x$

$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 4 } { 3 } } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 4 } { 3 } } \\ - 2 x + 3 y = - 2 \end{cases}$

$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 4 } { 3 } } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 4 } { 3 } } \\ \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 2 } \end{cases}$

$ $ Substitute the given $ x $ value into the equation $ - 2 x + 3 y = - 2$

$\color{#FF6800}{ - } \color{#FF6800}{ 2 } \left ( \color{#FF6800}{ \dfrac { 4 } { 3 } } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 4 } { 3 } } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 3 } \color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 2 }$

$ $ Solve a solution to $ y$

$\color{#FF6800}{ y } = \color{#FF6800}{ 2 }$

$ $ Substitute the given $ y $ value into the equation $ x = \dfrac { 4 } { 3 } y + \dfrac { 4 } { 3 }$

$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 4 } { 3 } } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 4 } { 3 } }$

$x = \color{#FF6800}{ \dfrac { 4 } { 3 } } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } + \dfrac { 4 } { 3 }$

$ $ Calculate the product of rational numbers $ $

$x = \color{#FF6800}{ \dfrac { 8 } { 3 } } + \dfrac { 4 } { 3 }$

$x = \color{#FF6800}{ \dfrac { 8 } { 3 } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 4 } { 3 } }$

$ $ Find the sum of the fractions $ $

$x = \color{#FF6800}{ 4 }$

$\color{#FF6800}{ x } = \color{#FF6800}{ 4 }$

$ $ The possible solutions are as follows $ $

$\color{#FF6800}{ x } = \color{#FF6800}{ 4 } , \color{#FF6800}{ y } = \color{#FF6800}{ 2 }$

$ $ Check if it is the solution to the system of equations $ $

$\begin{cases} \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 4 } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } = \color{#FF6800}{ 4 } \\ \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 4 } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } = \color{#FF6800}{ - } \color{#FF6800}{ 2 } \end{cases}$

$ $ Simplify the equality $ $

$\begin{cases} \color{#FF6800}{ 4 } = \color{#FF6800}{ 4 } \\ \color{#FF6800}{ - } \color{#FF6800}{ 2 } = \color{#FF6800}{ - } \color{#FF6800}{ 2 } \end{cases}$

$ $ Since it is true in both equations, it is the solution of the system of equations $ $

$\color{#FF6800}{ x } = \color{#FF6800}{ 4 } , \color{#FF6800}{ y } = \color{#FF6800}{ 2 }$

Solution search results