Name: Alexander
Grade 11
Student asking questions!

Hello, i have a math assignment due tonight at midnight and i need some help please

It is using the addition method to solve linear systems

1.
-2x+5y=-3
2x-3y=-1


2.
8c-3d=-10
2c-5d=6

3.
6x+5y=22
3y=4x+36


Can you please solve these and show me the steps by email?

Thanks

Alexander

Alexander,

I think I know what you mean by "the addition method" so let me illustrate with a different pair of equations.

3x + y = -5
6x - 5y = 4

The technique is to select one of the variables, either x or y, and manipulate the equations so that the coefficients of this variable in the two equations have the same value except with opposite signs. So, for example if I multiply both sides of the first equation by 5 then the coefficients of y in the two equations become 5 and -5. I could also multiply the first equation by -2 and then the coefficients of x in the two equations are 6 and -6. I am going to choose that latter.

Multiply both sides of the first equation by -2 to get

-6x - 2y = 10
6x - 5y = 4

Now add the two equations to get

0x - 7y = 14 so -7y = 14 and hence y = -2

Now substitute this value into either of the original equations (I am going to use the first equation) and solve for x.

3x + y = -5 so 3x -2 = -5 or 3x = -3 and hence x = -1.

Hence my answer is x = -1, y = -2. You can verify this answer by substituting these values in the second equation to confirm that it is satisfied.

Penny