we are doing sloving system of linear equations by substituting

1)y=5x 2x+3y=34 i got (2,10)

2)x=4y 2x+3y=44 i got (16,4)

3)x=4y+5 x=3y-2 i got (-23,-7)

4)y=2x+3 y=4x-1 i got (2,7)

5)4c=3d+3 c=d-1 i got (6,7)

all correct.

continued

4c=3d+3 c=d-1 i got (6,7)

x=1/2y+3 2x-y=6 i got no solution

8x+2y=13 4x+y=11 i got no solution

2x-y=-4 -3x+y=-9 i got (13,30)

3x-5y=11 x-3y=1 i got (7,2)

subtititoin what is number 4y-2x=6 and 8y=4x-12

To solve systems of linear equations by substituting, you need to follow these steps:

1. Rewrite one of the equations in terms of a single variable.
2. Substitute the expression from step 1 into the other equation.
3. Solve the resulting equation for the remaining variable.
4. Substitute the value found in step 3 back into the expression from step 1.
5. Solve the resulting equation for the initially chosen variable.
6. Check the solution by substituting the values into both original equations.

Now, let's go through each of the given examples to see how to apply these steps:

1. For the system:
Equation 1: y = 5x
Equation 2: 2x + 3y = 34

From Equation 1, substitute y with 5x in Equation 2:
2x + 3(5x) = 34

Simplify and solve for x:
2x + 15x = 34
17x = 34
x = 34/17
x = 2

Substitute the value of x back into Equation 1:
y = 5(2)
y = 10

The solution to the system is (2, 10).

2. For the system:
Equation 1: x = 4y
Equation 2: 2x + 3y = 44

From Equation 1, substitute x with 4y in Equation 2:
2(4y) + 3y = 44

Simplify and solve for y:
8y + 3y = 44
11y = 44
y = 44/11
y = 4

Substitute the value of y back into Equation 1:
x = 4(4)
x = 16

The solution to the system is (16, 4).

3. For the system:
Equation 1: x = 4y + 5
Equation 2: x = 3y - 2

Equate the two expressions for x:
4y + 5 = 3y - 2

Simplify and solve for y:
4y - 3y = -2 - 5
y = -7

Substitute the value of y back into Equation 1:
x = 4(-7) + 5
x = -28 + 5
x = -23

The solution to the system is (-23, -7).

4. For the system:
Equation 1: y = 2x + 3
Equation 2: y = 4x - 1

Equate the two expressions for y:
2x + 3 = 4x - 1

Simplify and solve for x:
2x - 4x = -1 - 3
-2x = -4
x = -4/-2
x = 2

Substitute the value of x back into Equation 1:
y = 2(2) + 3
y = 4 + 3
y = 7

The solution to the system is (2, 7).

5. For the system:
Equation 1: 4c = 3d + 3
Equation 2: c = d - 1

From Equation 2, substitute c with d - 1 in Equation 1:
4(d - 1) = 3d + 3

Simplify and solve for d:
4d - 4 = 3d + 3
4d - 3d = 3 + 4
d = 7

Substitute the value of d back into Equation 2:
c = 7 - 1
c = 6

The solution to the system is (6, 7).

Remember to always check your solutions by substituting them into both original equations.