Algebra

System of Linear Equations

System of Linear Equations - More Variables

         

Consider a system of linear equations x+y=3,y+z=11,z+x=20.\begin{aligned} x+y &= 3, \\ y+z &= 11, \\ z+x &= 20. \end{aligned} What is the value of 3x+y+5z3x+y+5z?

Let x=ax=a, y=by=b and z=cz=c be the values of xx, yy and zz, respectively, that satisfy the system of linear equations xy=3y+z=25zx=8. \begin{aligned} x-y&=3 \\ y+z&=25 \\ z-x&=8. \end{aligned} What is the value of a+b+ca+b+c?

Let x=ax=a, y=by=b and z=cz=c be the values of xx, yy and zz, respectively, that satisfy the system of linear equations x+2y=242y+3z=58x+3z=38. \begin{aligned} x+2y&= 24 \\ 2y+3z&= 58\\ x+3z&= 38. \end{aligned} What is the value of a+b+ca+b+c?

Let x=ax=a, y=by=b and z=cz=c be the values of xx, yy and zz, respectively, that satisfy the system of linear equations 3x2=y+13=2z15,3x+2y+z=65. \frac{3-x}{2}= \frac{y+1}{3}=\frac{2z-1}{5}, \, 3x+2y+z=65. What is the value of a+b+ca+b+c?

Let x=Ax=A, y=By=B and z=Cz=C be the solutions of the simultaneous equations x+y+z=270xy+z=90x+yz=0.\begin{aligned} x+y+z &= 270 \\ x-y+z &= 90 \\ x+y-z &=0. \end{aligned} What is the value of A+BC\frac{A+B}{C}?

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