Q. Find the solution of the system of equations.−x+6y−8x−3y=23=31(□,□)
Write Equations: Write down the system of equations to be solved.We have the following system of equations:1) −x+6y=232) −8x−3y=31We will use the method of substitution or elimination to find the values of x and y that satisfy both equations.
Choose Solution Method: Decide which method to use for solving the system.We can use either substitution or elimination. In this case, we will use the elimination method because it seems straightforward to eliminate x by multiplying the first equation by 8 and adding it to the second equation.
Multiply First Equation: Multiply the first equation by 8 to prepare for elimination.Multiplying the first equation by 8 gives us:8(−x+6y)=8(23)Which simplifies to:−8x+48y=184
Add Equations for Elimination: Add the new equation to the second equation to eliminate x. We add −8x+48y=184 (from Step 3) to −8x−3y=31 (the second original equation): (−8x+48y)+(−8x−3y)=184+31 This simplifies to: −16x+45y=215