The given set of equations are linear and equivalent, resulting in infinitely many solutions. This outcome is demonstrable both graphically, where the plotted lines coincide, and arithmetically, where equating the normalized equations yields no unique solution.
To solve these equations both graphically and arithmetically, you first need to put the equations into slope-intercept form (y = mx+b), where m is the slope and b is the y-intercept.
Equation 1: 4x - 8y = -4 turns into y = 0.5x + 0.5
Equation 2: 7x - 14y = - 7 turns into y = 0.5x + 0.5
Graphical Solution: To solve these equations graphically, you can plot both lines on a graph and look for the point where they intersect. This is your solution. In this case, as both equations simplify to the same equation, the lines will coincide (lie on top of each other), meaning there are infinitely many solutions.
Arithmetic Solution: Set the equations equal to each other and solve for x. As the equations are identical, there is no unique solution for x, again providing evidence for infinitely many solutions.
Learn more about Solving Linear Equations