# SOLUTION: 1. 4x+3y=1, x=1-y 2. 2x-y=6, -x+y=-1 3. 6x-y=3, 4x-2y=-2 4. 2x+3y=7, x=1-4y 5. 2x+3y=6, x-3y=-15 6. 7x-5y=4, y=3x-4 7. 2y-5x=-1, x=2y+5 8. 4x+3y=1, 3x+4y=10 9. 6x-5y=3, 4x+

Algebra ->  Algebra  -> Coordinate Systems and Linear Equations -> SOLUTION: 1. 4x+3y=1, x=1-y 2. 2x-y=6, -x+y=-1 3. 6x-y=3, 4x-2y=-2 4. 2x+3y=7, x=1-4y 5. 2x+3y=6, x-3y=-15 6. 7x-5y=4, y=3x-4 7. 2y-5x=-1, x=2y+5 8. 4x+3y=1, 3x+4y=10 9. 6x-5y=3, 4x+      Log On

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 Click here to see ALL problems on Linear-systems Question 1088: 1. 4x+3y=1, x=1-y 2. 2x-y=6, -x+y=-1 3. 6x-y=3, 4x-2y=-2 4. 2x+3y=7, x=1-4y 5. 2x+3y=6, x-3y=-15 6. 7x-5y=4, y=3x-4 7. 2y-5x=-1, x=2y+5 8. 4x+3y=1, 3x+4y=10 9. 6x-5y=3, 4x+3y=21 10. x+y=4, 3x+4y=10 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. Answer by AnlytcPhil(1277)   (Show Source): You can put this solution on YOUR website!I'll just solve #2 and #9. All are similar to these two: 2. 2x-y=6 -x+y=-1 Substitution method: Pick one of the unknowns and an equation that contains it. You can actually choose either letter and either equation it's in. However things will be simpler if one of the equations contains +x, -x, +y, or -y, and you choose that letter and that equation. We have three good choices in this problem, so I'll arbitrarily pick y and the second equation: 1. Solve the chosen equation for the chosen letter -x + y = -1 y = -1 + x 2. Replace the chosen letter in the OTHER equation by the expression which that letter equals from step 1. Solve for the OTHER letter. 2x - y = 6 2x - (-1 + x) = 6 2x + 1 - x = 6 x + 1 = 6 x = 6 - 1 x = 5 3. Substitute that value for that letter into the result of step 1: y = -1 + x y = -1 + (5) y = 4 ---------------------------------- 9. 6x-5y=3, 4x+3y=21 1. Rearrange the terms of the equations so that like terms line up vertically like this: Ax + By = C Dx + Ey = F ---------------------- 6x - 5y = 3 4x + 3y = 21 ---------------------- 2. Get the LCM (least common multiple) of the coefficients of x in absolute value. The LCM of 6 and 4 is 12. 3. Multiply each equation by whatever number is necessary to cause the coefficient of x to be equal to the LCD. The equation 6x - 5y = 3 needs to be multiplied by 2 to make the coefficient of x to be 12 2[ 6x - 5y = 3] 12x - 10y = 6 The equation 4x + 3y = 21 needs to be multiplied by 3 to make the coefficient of x to be 12 3[4x + 3y = 21] 12x + 9y = 63 Since these both have +12x I will pick the second one to multiply through by -1, getting -12x - 9y = -63, so now we have this system: 12x - 10y = 6 -12x - 9y = -63 Now add vertically 12x - 10y = 6 -12x - 9y = -63 ----------------- -19y = -57 y = -57/(-19) y = 3 4. Go back to where the terms of the equations are arranged so that like terms line up vertically like this: Ax + By = C Dx + Ey = F 6x - 5y = 3 4x + 3y = 21 2. Get the LCM (least common multiple) of the coefficients of y in absolute value. The LCM of 5 and 3 is 15. 3. Multiply each equation by whatever number is necessary to cause the coefficient of x to be equal to the LCD in absolute value: The equation 6x - 5y = 3 needs to be multiplied by 3 to make the coefficient of y have absolute value 15 3[ 6x - 5y = 3] 18x - 15y = 9 The equation 4x + 3y = 21 needs to be multiplied by 5 to make the coefficient of y to be 15 in absolute value 5[4x + 3y = 21] 20x + 15y = 105 Since these already have their y terms equal in absolute value but opposite in sign, I don't need to multiply either one through by -1. So now we have this system: 18x - 15y = 9 20x + 15y = 105 Now add vertically 18x - 15y = 9 20x + 15y = 105 ----------------- 38x = 114 y = 114/38 y = 3 ------------------ Here are the answers to all your systems: 1. 4x+3y=1, x=1-y ---- answer x=-2, y=3 2. 2x-y=6, -x+y=-1 --- x=5, y=4 3. 6x-y=3, 4x-2y=-2 -- x=1, y=3 4. 2x+3y=7, x=1-4y --- x=5, y=-1 5. 2x+3y=6, x-3y=-15 - x=-3, y=4 6. 7x-5y=4, y=3x-4 --- x= 2, y=2 7. 2y-5x=-1, x=2y+5 -- x=27, y=11 8. 4x+3y=1, 3x+4y=10 - x=-26/7, y = 37/7 9. 6x-5y=3, 4x+3y=21 - x=3, y=3 10. x+y=4, 3x+4y=10 - x=6, y=-2 Edwin