Calculator search results

Formula

Solve the system of equations

Answer

Graph

$4 x + 3 y = 5$

$3 x - 4 y = 10$

$x$Intercept

$\left ( \dfrac { 5 } { 4 } , 0 \right )$

$y$Intercept

$\left ( 0 , \dfrac { 5 } { 3 } \right )$

$x$Intercept

$\left ( \dfrac { 10 } { 3 } , 0 \right )$

$y$Intercept

$\left ( 0 , - \dfrac { 5 } { 2 } \right )$

$\begin{cases} 4x+3y = 5 \\3x-4y = 10 \end{cases}$

$x = 2 , y = - 1$

Solve the system of equations

$\begin{cases} 4 x + 3 y = 5 \\ 3 x - 4 y = 10 \end{cases}$

$ $ Solve a solution to $ x$

$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 3 } { 4 } } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 5 } { 4 } } \\ 3 x - 4 y = 10 \end{cases}$

$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 3 } { 4 } } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 5 } { 4 } } \\ \color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ y } = \color{#FF6800}{ 10 } \end{cases}$

$ $ Substitute the given $ x $ value into the equation $ 3 x - 4 y = 10$

$\color{#FF6800}{ 3 } \left ( \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 3 } { 4 } } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 5 } { 4 } } \right ) \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ y } = \color{#FF6800}{ 10 }$

$ $ Solve a solution to $ y$

$\color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 1 }$

$ $ Substitute the given $ y $ value into the equation $ x = - \dfrac { 3 } { 4 } y + \dfrac { 5 } { 4 }$

$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 3 } { 4 } } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 5 } { 4 } }$

$x = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 3 } { 4 } } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) + \dfrac { 5 } { 4 }$

$ $ Calculate the product of rational numbers $ $

$x = \color{#FF6800}{ \dfrac { 3 } { 4 } } + \dfrac { 5 } { 4 }$

$x = \color{#FF6800}{ \dfrac { 3 } { 4 } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 5 } { 4 } }$

$ $ Find the sum of the fractions $ $

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

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

$ $ The possible solutions are as follows $ $

$\color{#FF6800}{ x } = \color{#FF6800}{ 2 } , \color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 1 }$

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

$\begin{cases} \color{#FF6800}{ 4 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) = \color{#FF6800}{ 5 } \\ \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) = \color{#FF6800}{ 10 } \end{cases}$

$ $ Simplify the equality $ $

$\begin{cases} \color{#FF6800}{ 5 } = \color{#FF6800}{ 5 } \\ \color{#FF6800}{ 10 } = \color{#FF6800}{ 10 } \end{cases}$

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

$\color{#FF6800}{ x } = \color{#FF6800}{ 2 } , \color{#FF6800}{ y } = \color{#FF6800}{ - } \color{#FF6800}{ 1 }$

Solution search results

$2$ Find the values of following determinants. $\left(1\right)$ $|^{-1}$ $2$ $7$ $4$ $\left(2\right)$ $ \begin{cases} 5 \\ -7 \end{cases} $ $3$ $\left(3\right)$ $0$ $3.$ Solve the following simultaneous equations $\left(1\right)$ $3x-4y=10:4x+3y=5$ $\left(2\right)$ $4x$

10th-13th grade

Algebra

Check solution

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