Question

1 ) Solve the system of equations by substitution.

x + y = 6
y = 5x

2 ) Solve the system using substitution.
y = -6x + 36
6y - x + 6 = 0

3 ) Solve by the substitution method.
5x + 9y = -13
-6x + y = 51

Answer 1

1) x=1, y=5
2) x=6, y=0

3) x = -8, y = 99

Explanation:

1)
x + 5x = 6

6x = 6

x = 1

y = 5

2)

y = -6x + 36

6y - x + 6 = 0

6(-6x + 36) - x + 6 = 0

-37x + 222 = 0

x = 6

y = 0

3)

5x + 9y = -13

-6x + y = 51

y = 6x + 51

5x + 9(6x + 51) = -13

59x + 459 = -13

x = -8

y = 99

Answer 2

x = -8 and y = 3

Explanation:

Solve the system of equations by substitution:

x + y = 6

y = 5x

Substitute the value of y from the second equation into the first equation:

x + (5x) = 6

6x = 6

x = 1

Now, substitute the value of x into the second equation to find y:

y = 5(1)

y = 5

So, the solution to the system of equations is x = 1 and y = 5.

Solve the system using substitution:

y = -6x + 36

6y - x + 6 = 0

Substitute the value of y from the first equation into the second equation:

6(-6x + 36) - x + 6 = 0

-36x + 216 - x + 6 = 0

-37x + 222 = 0

-37x = -222

x = 6

Now, substitute the value of x into the first equation to find y:

y = -6(6) + 36

y = -36 + 36

y = 0

So, the solution to the system of equations is x = 6 and y = 0.

Solve by the substitution method:

5x + 9y = -13

-6x + y = 51

Rearrange the second equation to isolate y:

y = 6x + 51

Substitute the value of y from the second equation into the first equation:

5x + 9(6x + 51) = -13

5x + 54x + 459 = -13

59x + 459 = -13

59x = -472

x = -8

Now, substitute the value of x into the second equation to find y:

y = 6(-8) + 51

y = -48 + 51

y = 3

So, the solution to the system of equations is x = -8 and y = 3.