Solve using the substitution method of { x/2 + y/3 = 5, x - y/2 = 4 }

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

Solve using the elimination method of { x/2 + y/3 = 5, x - y/2 = 4 }

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

Solve using the Gauss-Jordan method of { x/2 + y/3 = 5, x - y/2 = 4 }

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

Solve using the Cramer's rule of { x/2 + y/3 = 5, x - y/2 = 4 }

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

Determine whether lines are parallel, perpendicular, or neither of { x/2 + y/3 = 5, x - y/2 = 4 }

\textrm{Neither parallel nor perpendicular}

Question :

x/2 + y/3 = 5, x - y/2 = 4

Solve the system of equations

Solve using the substitution method

Solve using the elimination method

Solve using the Gauss-Jordan method

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

Alternative Form

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

Evaluate

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

Calculate

More Steps

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

Calculate

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

Solve the equation for x

More Steps

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

Substitute the given value of x into the equation \frac{x}{2} + \frac{y}{3} = 5

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

Divide the terms

More Steps

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

Multiply both sides of the equation by LCD

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

Simplify the equation

More Steps

24 + 7 y = 5 \times 12

Simplify the equation

24 + 7 y = 60

Move the constant to the right side

7 y = 60 - 24

Subtract the numbers

7 y = 36

Divide both sides

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

Divide the numbers

y = \frac{36}{7}

Substitute the given value of y into the equation x = \frac{8 + y}{2}

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

Calculate

x = \frac{46}{7}

Calculate

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

Check the solution

More Steps

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

Solution

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

Alternative Form

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

Show Solution

Relationship between lines

Neither parallel nor perpendicular

Show Solution

x/2 + y/3 = 5, x - y/2 = 4

Solve the system of equations

Relationship between lines

Graph

Frequently Asked Questions

Solve using the substitution method of \({ x/2 + y/3 = 5, x - y/2 = 4 }\)

Solve using the elimination method of \({ x/2 + y/3 = 5, x - y/2 = 4 }\)

Solve using the Gauss-Jordan method of \({ x/2 + y/3 = 5, x - y/2 = 4 }\)

Solve using the Cramer's rule of \({ x/2 + y/3 = 5, x - y/2 = 4 }\)

Determine whether lines are parallel, perpendicular, or neither of \({ x/2 + y/3 = 5, x - y/2 = 4 }\)