Question

Systems of equation PLEASE HELP!! questions attached below

Answer 1

Question 1:

For this case we have we have the following system of equations:

`y = 3x-4\\x-4y = -28`

We substitute the first equation in the second one:

`x-4 (3x-4) = - 28\\x-12x + 16 = -28\\-11x = -28-16\\-11x = -44\\x = \frac {-44} {- 11}\\x = 4`

We look for the value of "y":

`y = 3x-4\\y = 3 (4) -4\\y = 12-4\\\y = 8`

Finally, the solution of the system is:

`(x, y) :( 4,8)`

ANswer:

`(x, y) :( 4,8)`

Question 2:

For this case we have we have the following system of equations:

`2x-3y = 13x-4y\\-3x-2y = 0`

We manipulate the first equation:

`-3y + 4y = 13x-2x\\y = 11x`

We substitute in the second equation:

`-3x-2 (11x) = 0\\-3x-22x = 0\\-25x = 0\\x = 0`

We look for the value of "y":

`y = 11 (0) = 0`

Finally, the solution of the system is:

`(x, y) :( 0,0)`

ANswer:

`(x, y) :( 0,0)`

Question 3:

For this case we have we have the following system of equations:

`y = 4x-1\\y = -2x-7`

Equating the equations:

`4x-1 = -2x-7\\4x + 2x = -7 + 1\\6x = -6\\x = \frac {-6} {6}\\x = -1`

We look for the value of "y":

`y = 4x-1\\y = 4 (-1) -1\\y = -4-1\\y = -5`

Finally, the solution of the system is:

`(x, y): (- 1, -5)`

ANswer:

`(x, y): (- 1, -5)`

Answer 2

Q 19) x = 4; y = 8.

Q 20) x = 0 ; y = 0.

Q 21) x = -1; y = -5.

Explanation:

Q 19)

y = 3x - 4 (Equation 1)

x - 4y = -28 (Equation 2)

Put Equation 2 in Equation 1:

x - 4(3x - 4) = -28.

x - 12x + 16 = -28

-11x = -44.

x = -44/-11.

x = 4.

Put x = 4 in Equation 1:

y = 3(4) - 4.

y = 12 - 4.

y = 8.

Q 20)

2x - 3y = 13x - 4y (Equation 1)

-3x - 2y = 0 (Equation 2).

From Equation 2:

-2y = 3x.

y = -3x/2 (Equation 3).

Put Equation 3 in Equation 1:

2x - 3(-3x/2) = 13x - 4(-3x/2).

2x + 4.5x = 13x + 6x.

12.5x = 0.

x = 0.

Put x = 0 in Equation 3:

y = 0.

Q 21)

y = 4x - 1 (Equation 1).

y = -2x - 7 (Equation 2).

Since y = y, therefore:

4x - 1 = -2x - 7.

6x = -6.

x = -1.

Put x = -1 in Equation 1:

y = 4(-1) - 1.

y = -4 - 1.

y = -5.

In short:

Q 19) x = 4; y = 8!!!

Q 20) x = 0 ; y = 0!!!

Q 21) x = -1; y = -5!!!