How do I solve these systems algebraically?

Question

6x-4y=8
9x+5y=23
and
4x+3y=78
9x+20y=96

Answer 1

Find multipliers that, when applied, will cause one of the variable to drop out when the equations are added. For example, in your first set of equations, multiply the top equation by -1.5 and you get

-9x + 6y = -12
9x + 5y = 23

Add the equations:
11y = 11

and solve for the single variable. Now that you have that answer, plug it back into either of ther original equations and solve for the other variable


P.S. The multipliers aren't critical. You could have, for example, multiplied the first equation by 5 and the second equation by 4 yielding

30x - 20y = 40
36x + 20y = 92

Again, add equations (eliniating one variable), solve for the remaining variable, substitute the result back into one of the original equations, and solve for the other variable.

Answer 2

In Mathematics simultaneous equations are a set of equations containing multiple variables. This set is often referred to as a system of equations. To solve simultaneous equations, the solver needs to use the provided equations to find the exact value of each variable. Generally the solver uses either a graphical method (by plotting all the lines and/or curves on the same graph and finding the exact coordinates of their intersection), the matrix method, the substitution method, the elimination method, and the adding method.

Source: Lot of them at Internet...

Answer 3

1) 6x - 4y = 8
3x - 2y = 4

2) 9x + 5y = 23

Multiply modified eq 1 by -3 and add it to eq 2

-9x + 6y = - 12
9x + 5y = 23
- - - - - - - - - - -
11y = 11
y = 1

2) 9x + 5(1) = 23
9x + 5 = 23
9x = 18
x = 2

Check

1) 6(2) - 4(1) = 8
12 - 4 = 8
8 = 8

Answer 4

9x-6y=12
-
9x+5y=23

-11y=-11
y=1
x=(8+4)/6
x=2
Result: x=2, y=1

2-nd
x=(78-3y)/4
9(78-3y)/4+20y=96
9(78-3y)+80y=384
702-27y+80y=384
53y= -318
y= -6
x=(78-3(-6))/4
x=15
result: x=15, y= -6

Answer 5

For the first set...

multiply the first equation by 3 and the second by 2, the subtract

18x-12y=24
-(18x+10y=46)
----------------------------------
-22y=22
y=1

then plug y in to one of the original equations to get x
9x+5(1)=23
9x=18
x=2

for the second one, multiply the first one by 9 and the second on eby four, then subtract

36x+27y=702
36x+80y=384
------------------------------------

-53y=318
y=-6

then substitute-

4x-3(-6)=78
4x=60
x=15

voila!