Question

Solve the system of equations

3x + 4y + 2z = 1
4x + 6y + 2z = 7
2x + 3y + z = 11

Answer 1

Hindi ko po alam yan sorry

Answer 2

no solution

Explanation:

`\left\{\begin{matrix}3x+4y+2z=1\\4x+6y+2z=7\\2x+3y+z=11\\\end{matrix}\right.`

Rearrange

`\left\{\begin{matrix}3x+4y+2z=1\\4x+6y+2z=7\\z=11-2x-3y\\\end{matrix}\right.`

Substitute into one of the equations

`\left\{\begin{matrix}3x+4y+2(11-2x-3y)=1\\4x+6y+2(11-2x-3y)=7\\\end{matrix}\right.`

Apply the Distributive Property

`\left\{\begin{matrix}3x+4y+22-4x-6y=1\\4x+6y+22-4x-6y=7\\\end{matrix}\right.`

Apply the Inverse Property of Addition

`6y+22-6y=7`

`\left\{\begin{matrix}3x+4y+22-4x-6y=1\\22=7\\\end{matrix}\right.`

Rearrange variables to the left side of the equation

`\left\{\begin{matrix}3x+4y-4x-6y=1-22\\22=7\\\end{matrix}\right.`

Combine like terms

`\left\{\begin{matrix}-x-2y=1-22\\22=7\\\end{matrix}\right.`

Calculate the sum or difference

`\left\{\begin{matrix}-x-2y=-21\\22=7\\\end{matrix}\right.`

Rearrange like terms to the same side of the equation

`\left\{\begin{matrix}-x=-21+2y\\22=7\\\end{matrix}\right.`

Divide both sides of the equation by the coefficient of variable

`\left\{\begin{matrix}x=21-2y\\22=7\\\end{matrix}\right.`

Based on the given conditions, the (system of) equation(s) has

`no\ solution`

I hope this helps you

:)