# Math

posted by .

How do I solve these problems, I really need help.

Solve by substitution method

6x+5y=17
x=53-8y

Solve by elimination method

2x+3y=5
4x+6y=10

• Math -

Substitution method:

6x+5y=17
x=53-8y

Solve for a variable and substitute it in to one of the equations. The easiest way with these two equations is to take x from the second equation and substitute it in to the first equation.

6(53-8y)+5y = 17

618 - 48y + 5y = 17
-48y + 5y = 17 - 618
-43y = -601
y = -601/-43

Then you plug y in to one of the equations and solve for x.

x = 53 - 8*(601/43)

Elimination method: The idea is you multiply one equation by a constant so either x or y has the same coefficient as the x or y in the other equation.

Example:

#1) x + 3y = 4
#2) 5x + 2y = -19

We need to pick a variable to eliminate. The easiest way is to eliminate the x in the second equation. To do this we multiply the first equation by 5 and subtract it from the second.

5*(x+3y) = 5*4
5x+15y = 20

It's tricky to write out the next part online, you normally write the equations directly over each other with a subtraction sign.

5x + 2y - 5x - 15y = -19 - 20
-13y = -39

At this point you can easily solve for y.

y = -39/-13 = 3

Then substitute y=3 in to one of the first equations.

x + 3y = 4
x + 3*3 = 4
x + 9 = 4
x = 4 -9
x = -5

--The problem you gave is slightly different.

2x+3y=5
4x+6y=10

In this problem you'd multiply the first equation by 2 and subtract it from the second. The new second equation is then 0 = 0.

This set of equations is not solvable. Using the elimination method one of the equations is completely eliminated because they are equivalent equations.

• math -

how do you do this equation by using elimination.? 8x-5y=11
4x-3y=5