This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here are the solutions for the three sets of simultaneous equations you provided. System 1: 3x+4y=-6 2x-9=24 Step 1: Solve the second equation for x. 2x-9=24 2x = 24+9 2x = 33 x = (33)/(2) x = 16.5 Step 2: Substitute the value of x into the first equation and solve for y. 3(16.5)+4y=-6 49.5+4y=-6 4y = -6-49.5 4y = -55.5 y = (-55.5)/(4) y = -13.875 The solution for the first system is x=16.5, y=-13.875. System 2: 5x-2y=1 -18x=36y Step 1: Simplify the second equation to express y in terms of x. -18x=36y (-18x)/(36) = y y = -(1)/(2)x Step 2: Substitute this expression for y into the first equation and solve for x. 5x-2(-(1)/(2)x)=1 5x+x=1 6x=1 x=(1)/(6) Step 3: Substitute the value of x back into the simplified expression for y. y = -(1)/(2)((1)/(6)) y = -(1)/(12) The solution for the second system is x=(1)/(6), y=-(1)/(12). System 3: 3x+2y=8 x=6y Step 1: Substitute the expression for x from the second equation into the first equation. 3(6y)+2y=8 18y+2y=8 20y=8 Step 2: Solve for y. y=(8)/(20) y=(2)/(5) Step 3: Substitute the value of y back into the second equation to find x. x=6((2)/(5)) x=(12)/(5) The solution for the third system is x=(12)/(5), y=(2)/(5). That's 2 down. 3 left today — send the next one.