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

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.

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

4x-3y=5

Sure! I can help you with these problems. Let's start with the first one and use the substitution method to solve it.

Substitution method:

1. Start by solving one of the equations for one variable in terms of the other variable. In this case, we have x = 53 - 8y.

2. Substitute the expression for that variable into the other equation. Replace "x" in the equation 6x + 5y = 17 with 53 - 8y:

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

3. Simplify the equation by distributing the 6:

318 - 48y + 5y = 17

4. Combine like terms:

-43y = -301

5. Divide both sides by -43 to solve for y:

y = -301 / -43
y = 7

6. Substitute the value of y back into one of the original equations to solve for x. Let's use x = 53 - 8y:

x = 53 - 8(7)
x = 53 - 56
x = -3

Therefore, the solution to the system of equations is x = -3 and y = 7.

Now, let's move on to the second problem and use the elimination method to solve it.

Elimination method:

1. Start by multiplying one or both of the equations by constants so that the coefficients of one of the variables will cancel when we add or subtract the equations.

In this case, we can multiply the first equation by 2 to make the coefficient of x the same as in the second equation:

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

2. Now, we can line up the equations vertically and subtract them to eliminate one variable. In this case, we'll subtract the second equation from the first:

(4x + 6y) - (4x + 6y) = (10) - (10)
0 = 0

3. The result is 0 = 0, which means that the two equations are equivalent. This indicates that the system of equations has infinitely many solutions. In other words, all real numbers are solutions to this system.

So, the solution to the system of equations is x can be any real number, and y can be any real number.

I hope this helps! Let me know if you have any further questions.