Algebra
Solving Equations
Solve the following system of equations: \[\begin{cases} 2x+y=7 \\ 4x-y=5. \end{cases}\]
Solve the following system of equations: \[\begin{cases} -3x+4y=29 \\ -7x-4y=1. \end{cases}\]
Let \( x = a\) and \(y = b\) be the solution of the following system of linear equations: \[x-y=7,\quad 3x+2y=26.\] What is the value of \(a+b\)?
Given that \(x\) and \(y\) are real numbers satisfying the equations \(3x - 2y = 22\) and \(7x + 3y = 105\), what is the value of \(x+y\)?
Solve the following system of equations: \[\begin{cases} 6x+2y=42 \\ 8x-4y=36. \end{cases}\]