Solve by using linear combination NOT Substitution Method: -5x+3y+z=-15 10x+2y+8z=18 15x+5y+7z=9

⚑ Flag

Subtract the second equation from the third one.  This gives you 5X +3Y - Z = -9 Add this to the first original equation.  This gives you: 6Y = -24 since the X and Z terms cancel out. Y = -4 Replace the Y value in the fir equation and second equation with -4.  Now you have: -5X -12 + Z = -15 and 10X -8 + 8Z = 18 Multiply the first one of these new equations by -8.  This gives you : 40X +96 -8Z = 120.  Subtract 96 from both sides.  Now it is 40X - 8Z = 24     Add this to your new equation 2 like this: 40X - 8Z =24 10X + 8Z = 26    Addition of these two gives you 50X = 50 since the Z terms equal to zero. Now X = 1 Substitute X = 1 and Y = -4 into the top original equation: -5 -12 +Z = -15 to get Z = 2 So X = 1,  Y = -4,  and Z = 2 Check that your complete solution satisfies all three equations.  It does.  That's it!