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I need help, kinda confused I need a step by step preferably explained on paper

I need help, kinda confused I need a step by step preferably explained on paper-example-1
User Taway
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Answer:

By elimination method:

e.

4x - y = 0

12x - 6y = 24

We can use the method of substitution. From the first equation, we have y = 4x. We substitute this value of y into the second equation:

12x - 6(4x) = 24

12x - 24x = 24

-12x = 24

x = -2

Substituting the value of x back into the first equation:

4(-2) - y = 0

-8 - y = 0

y = -8

Therefore, the solution to the system of equations is x = -2 and y = -8.

f.

3x + 15y = 3

2x - 5y = -28

We can use the method of elimination. Multiply the first equation by 2 and the second equation by 3 to eliminate x:

6x + 30y = 6

6x - 15y = -84

Subtract the second equation from the first equation:

(6x + 30y) - (6x - 15y) = 6 - (-84)

45y = 90

y = 2

Substitute the value of y into one of the original equations:

3x + 15(2) = 3

3x + 30 = 3

3x = -27

x = -9

Therefore, the solution to the system of equations is x = -9 and y = 2.

g.

3x + 2y = 10

6x + 4y = 15

We can again use the method of elimination. Multiply the first equation by 2 to eliminate y:

6x + 4y = 20

6x + 4y = 15

Since the equations are the same, we have infinitely many solutions. This means that any values of x and y that satisfy the equation 3x + 2y = 10 will be a solution to the system. They are parallel.

h.

4x - 6y = -26

-2x + 3y = 13

Again, we can use the method of elimination. Multiply the second equation by 2 to eliminate x:

4x - 6y = -26

-4x + 6y = 26

Add the two equations:

0 = 0

Since the equations are equivalent, we also have infinitely many solutions. Any values of x and y that satisfy the equation 4x - 6y = -26 will be a solution to the system. They are the same straight line.

User Miguel Pereira
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