Elimination method

Question

Find the solution of the system of equations.

−2x−5y=-15

-9x+15y=-30

Answer 1

x=5, y = 1 is the solution

-9x+15y=-30 divide by 3

-3x +5y = -10 add the other equation to eliminate one variable

-2x-5y=-15

-5x = -25

x =5

-3(5) +5y = -10

5y= 5

y = 1

(x,y) = (5,1)

graph the two lines and find their intersection point (5,1) that's a good check on the answer

Answer 2

HI Charlee C

Notice the coefficients of the y variables already have opposite signs, so y can be eliminated if we multiply the first equation by 3

3(-2x-5y=-15) = -6x -15y = -45 now y can be eliminated

-6x -15y = -45

-9x + 15y = -30

Leaves

-15x= -75

x = 5

Now we can plug this back into one of the original equations and solve for y

-9x + 15y = -30

-9(5) + 15y = -30

-45 + 15y = -30

15y = 15

y = 1

Checking

-2x -5y = -15

-2(5) -5(1) = -15

-10 - 5 = -15

-15 = -15

-9x + 15y = -30

-9(5) + 15(1) = -30

-45 + 15 = -30

-30 = -30

Hope this helps

Answer 3

−2x−5y=-15

-9x+15y=-30

3*(−2x−5y=-15)

-9x+15y=-30

−6x−15y=-45

-9x+15y=-30

−15x=-75

x = 5 ; y = 1