Solve by eliminnation methods

2x-4y=5
2x-4y=6
solve the system by elimination method
5x+2y= -13
7x-3y=17
Solve
x+6<-7 or x+6>4
Determine whether the given numbers are solutions of the inequality
8,-10,-18,-3
y-8>2y-3
Solve by the substitutioj method
2m+n=9
m-5n=10

Please post such problems separately and show your work. If you are unfamiliar with the elimination and substitution methods for solving simultaneous equations, referenc material can be provided.

Your first question has no solution because the two equations are incompatible. They represent two parallel lines.

To solve the system of equations using the elimination method, we need to eliminate one variable by adding or subtracting the equations.

1) Solve the system:
2x - 4y = 5
2x - 4y = 6

By subtracting the second equation from the first equation, we can eliminate the variable "x":

(2x - 4y) - (2x - 4y) = 5 - 6
0 = -1

Since the equation 0 = -1 is not true, the system has no solution. The lines represented by the equations are parallel and do not intersect.

2) Solve the system:
5x + 2y = -13
7x - 3y = 17

To eliminate the variable "y", multiply the first equation by 3 and the second equation by 2:

3(5x + 2y) = 3(-13)
2(7x - 3y) = 2(17)

This gives us:
15x + 6y = -39
14x - 6y = 34

Now, add the equations together:

(15x + 6y) + (14x - 6y) = -39 + 34
29x = -5
x = -5/29

Substitute the value of x back into one of the original equations to find y:

5(-5/29) + 2y = -13
-25/29 + 2y = -13
2y = -13 + 25/29
2y = -377/29 + 25/29
2y = -352/29
y = -176/29

So, the solution to the system of equations is x = -5/29 and y = -176/29.

3) Solve the inequality:
x + 6 < -7 or x + 6 > 4

For the first inequality:
x + 6 < -7
Subtract 6 from both sides:
x < -7 - 6
x < -13

For the second inequality:
x + 6 > 4
Subtract 6 from both sides:
x > 4 - 6
x > -2

Therefore, the solution to the inequality is x < -13 or x > -2.

4) Determine whether the given numbers are solutions of the inequality y - 8 > 2y - 3:

For 8:
8 - 8 > 2(8) - 3
0 > 13 (false)

For -10:
-10 - 8 > 2(-10) - 3
-18 > -23 (true)

For -18:
-18 - 8 > 2(-18) - 3
-26 > -39 (true)

For -3:
-3 - 8 > 2(-3) - 3
-11 > -9 (false)

Therefore, the numbers -10 and -18 are solutions of the inequality.

5) Solve the system of equations using the substitution method:
2m + n = 9
m - 5n = 10

Rearrange the first equation to solve for n:
n = 9 - 2m

Substitute the value of n in the second equation:
m - 5(9 - 2m) = 10
m - 45 + 10m = 10
11m - 45 = 10
11m = 55
m = 55/11
m = 5

Substitute the value of m back into the first equation to find n:
2(5) + n = 9
10 + n = 9
n = 9 - 10
n = -1

So, the solution to the system of equations is m = 5 and n = -1.

To solve the system of equations using the elimination method, follow these steps:

1. Start by writing both equations in standard form, which is ax + by = c.

Equation 1: 2x - 4y = 5
Equation 2: 2x - 4y = 6

2. Notice that both equations have the same coefficients for x and y, so we can't eliminate any variables just yet. However, we can subtract one equation from the other to eliminate one variable.

Subtracting Equation 2 from Equation 1:
(2x - 4y) - (2x - 4y) = 5 - 6
0 = -1

Since 0 does not equal -1, we have a contradiction. Therefore, the system of equations is inconsistent, meaning there is no solution.

To solve the system of equations using the elimination method, follow these steps:

1. Start by writing both equations in standard form, which is ax + by = c.

Equation 1: 5x + 2y = -13
Equation 2: 7x - 3y = 17

2. Multiply Equation 1 by 3 and Equation 2 by 2 to make the coefficients of y the same.

Multiplying Equation 1 by 3: 15x + 6y = -39
Multiplying Equation 2 by 2: 14x - 6y = 34

3. Add the two equations together to eliminate y.

(15x + 6y) + (14x - 6y) = -39 + 34
29x = -5
x = -5/29

4. Substitute the value of x back into one of the original equations to solve for y. Let's use Equation 1.

5( -5/29) + 2y = -13
-25/29 + 2y = -13
2y = -13 + 25/29
2y = -377/29
y = -377/58

The solution to the system of equations is x = -5/29 and y = -377/58.

To solve the inequality x + 6 < -7 or x + 6 > 4, follow these steps:

1. Solve the first part of the inequality: x + 6 < -7

Subtract 6 from both sides:
x < -7 - 6
x < -13

2. Solve the second part of the inequality: x + 6 > 4

Subtract 6 from both sides:
x > 4 - 6
x > -2

The solution to the inequality is x < -13 or x > -2.

To determine whether the given numbers (8, -10, -18, -3) are solutions to the inequality y - 8 > 2y - 3, substitute each number into the inequality and see if it holds true.

For 8:
8 - 8 > 2(8) - 3
0 > 13
This is false, so 8 is not a solution.

For -10:
-10 - 8 > 2(-10) - 3
-18 > -23
This is true, so -10 is a solution.

For -18:
-18 - 8 > 2(-18) - 3
-26 > -39
This is true, so -18 is a solution.

For -3:
-3 - 8 > 2(-3) - 3
-11 > -9
This is true, so -3 is a solution.

Therefore, the numbers -10, -18, and -3 are solutions to the inequality.

To solve the system of equations using the substitution method, follow these steps:

1. Solve one of the equations for one variable in terms of the other variable.

Equation 1: 2m + n = 9
Equation 2: m - 5n = 10

Solving Equation 2 for m:
m = 10 + 5n

2. Substitute the expression for m from Equation 2 into Equation 1.

2(10 + 5n) + n = 9
20 + 10n + n = 9
11n = -11
n = -1

3. Substitute the value of n back into one of the original equations to solve for m. Let's use Equation 2.

m - 5(-1) = 10
m + 5 = 10
m = 5

The solution to the system of equations is m = 5 and n = -1.