Question

1.

2y = -2x + 6
x- 5y = -15

2.
5x + y = 2
20x + 3y = -4

please include a solution thank you.

Answer 1

1) (0, 3)

2) (-2, 12)

Explanation:

1)

2y = -2x + 6 → y = -x + 3

x - 5y = -15

Substitute the simplified first equation into the second equation and solve for x.

x - 5( -x + 3 ) = -15

x + 5x - 15 = -15

6x = 0

x = 0

Substitute into first equation to get y.

y = -(0) + 3

y = 3

The solution to the system is the coordinate (0, 3).

2)

5x + y = 2

20x + 3y = -4

Solve the first equation for y.

y = -5x + 2

Substitute this into the second equation and solve for x.

20x + 3 ( -5x + 2 ) = -4

20x - 15x + 6 = -4

5x = -10

x = -2

Substitute this value on the first equation to get y.

y = -5( -2 ) + 2

y = 10 + 2

y = 12

The solution to the system is the coordinate (-2, 12).

Answer 2

Explanation:

To solve the system of equations:

2y = -2x + 6 ----(1)

x - 5y = -15 ----(2)

We can use substitution method or elimination method. Here, we will use elimination method to eliminate y.

Multiplying equation (1) by -5, we get:

-10y = 10x - 30 ----(3)

Adding equations (2) and (3), we get:

-15y = -45

Dividing by -15 on both sides, we get:

y = 3

Substituting y = 3 in equation (2), we get:

x - 5(3) = -15

x - 15 = -15

Adding 15 on both sides, we get:

x = 0

Therefore, the solution of the system of equations is (x, y) = (0, 3).

To solve the system of equations:

5x + y = 2 ----(1)

20x + 3y = -4 ----(2)

We can use substitution method or elimination method. Here, we will use elimination method to eliminate y.

Multiplying equation (1) by -3, we get:

-15x - 3y = -6 ----(3)

Adding equations (2) and (3), we get:

5x = -10

Dividing by 5 on both sides, we get:

x = -2

Substituting x = -2 in equation (1), we get:

5(-2) + y = 2

-10 + y = 2

Adding 10 on both sides, we get:

y = 12

Therefore, the solution of the system of equations is (x, y) = (-2, 12).