Determine the equivalent system for the given system of equations. 4x − 5y = 2 3x − y = 8

Accepted Solution

Answer:Explanation:We have the following System of Linear Equations in two variables:[tex]\left \{ {4x-5y=2 \atop {3x-y=8}}\right.[/tex]So let's call this as SYSTEM A. Two systems of equations are said to be equivalen if and only if they have the same solution, so we can get an equivalent system, called SYSTEM B, by multiplying an equation by some constant value. Let's say we multiply equation (1) by 2, then:[tex]\left \{ {2(4x-5y=2) \atop {3x-y=8}}\right. \\ \\ \left \{ {8x-10y=4 \atop {3x-y=8}}\right.[/tex]In conclusion:SYSTEM A:[tex]\left \{ {4x-5y=2 \atop {3x-y=8}}\right.[/tex]SYSTEM B:[tex]\left \{ {8x-10y=4 \atop {3x-y=8}}\right.[/tex]SYSTEM A and SYSTEM B are equivalentLearn more:System of equations: