使用替换法求解 { x/2 + y/3 = 5, x - y/2 = 4 }

\left(x,y\right) = \left(\frac{46}{7},\frac{36}{7}\right)

使用消元法求解 { x/2 + y/3 = 5, x - y/2 = 4 }

\left(x,y\right) = \left(\frac{46}{7},\frac{36}{7}\right)

\left(x,y\right) = \left(\frac{46}{7},\frac{36}{7}\right)

\left(x,y\right) = \left(\frac{46}{7},\frac{36}{7}\right)

\textrm{Neither parallel nor perpendicular}

求值

{x \div 2 + y \div 3 = 5 x - y \div 2 = 4

计算

更多步骤

{\frac{x}{2} + \frac{y}{3} = 5 x - y \div 2 = 4

计算

{\frac{x}{2} + \frac{y}{3} = 5 x - \frac{y}{2} = 4

求解 x 的方程

更多步骤

{\frac{x}{2} + \frac{y}{3} = 5 x = \frac{8 + y}{2}

将 x 的给定值代入方程 \frac{x}{2} + \frac{y}{3} = 5

\frac{\frac{8 + y}{2}}{2} + \frac{y}{3} = 5

把各项相除

更多步骤

\frac{8 + y}{4} + \frac{y}{3} = 5

等式两边同时乘以LCD

(\frac{8 + y}{4} + \frac{y}{3}) \times 12 = 5 \times 12

简化方程

更多步骤

24 + 7 y = 5 \times 12

简化方程

24 + 7 y = 60

将常量移到右侧

7 y = 60 - 24

减去数字

7 y = 36

两边同时除以

\frac{7 y}{7} = \frac{36}{7}

把这些数相除

y = \frac{36}{7}

将 y 的给定值代入方程 x = \frac{8 + y}{2}

x = \frac{8 + \frac{36}{7}}{2}

计算

x = \frac{46}{7}

计算

{x = \frac{46}{7} y = \frac{36}{7}

检查解决方案

更多步骤

{x = \frac{46}{7} y = \frac{36}{7}

解题方案

(x, y) = (\frac{46}{7}, \frac{36}{7})

替代形式

(x, y) = (6. \dot{5} 7142 \dot{8}, 5. \dot{1} 4285 \dot{7})