Question

Solve the system of equations using the substitution method.

{2x+8y=4x=−3y+5



Enter your answers in the boxes.

X=?
Y=?

2.Solve the system of equations using the linear combination method.

{6g+8h=40−6g+2h=−20



Enter your answers in the boxes.
G=?
H=?

Answer 1

Answer: x = 14

y = - 3

Explanation:

the given system of equations is expressed as

2x+8y = 4- - - - - - - - - - - - - 1

x =−3y + 5- - - - - - - - - - - - 2

To apply the method of substitution, we would substitute equation 2 into equation 1, it becomes

2(- 3y + 5) + 8y = 4

- 6y + 10 + 8y = 4

Subtracting 10 from the left hand side and the right hand side of the equation, it becomes

- 6y + 10 - 10 + 8y = 4 - 10

- 6y + 8y = - 6

2y = - 6

Dividing the left hand side and the right hand side of the equation by 2, it becomes

2y/2 = - 6/2

y = - 3

Substituting y = - 3 into equation 2, it becomes

x = −3 × - 3 + 5

x = 9 + 5

x = 14

2) 2x+8y = 4- - - - - - - - - - - - - 1

x + 3y = 5- - - - - - - - - - - - 2

Multiplying equation 1 by 1 and equation 2 by 2, it becomes

2x + 8y = 4

2x + 6y = 10

Subtracting, it becomes

2y = - 6

y = - 6/2

y = - 3

Substituting y = - 3 into equation 2, it becomes

x + 3 × - 3 = 5

x - 9 = 5

x = 5 + 9 = 14

Answer 2

The answer to your question is 1.- (37/2, -9/2) 2.- g = 4 and h = 2

Explanation:

Data

Equation 1 2x + 8y = 1

Equation 2 x = -3y + 5

Process

1.- Substitute equation 2 in equation 1

2(-3y + 5) + 8y = 1

Expand

-6y + 10 + 8y = 1

Solve for y

8y - 6y = 1 - 10

2y = -9

y = -9/2

2.- Substitute y in equation 2 to find x

x = -3(-9/2) + 5

Simplify

x = 27/2 + 5

x = 27/2 + 10/2

x = 37/2

Solution (37/2, -9/2)

2.-

Equation 1 6g + 8h = 40

Equation 2 -6g + 2h = -20

Process

1.- Add both equations

Result

0 + 10h = 20

Solve for h

h = 20/10

h = 2

2.- Substitute h in Equation 1 to find g

6g + 8(2) = 40

Simplification

6g + 16 = 40

Solve for g

6g = 40 - 16

6g = 24

g = 24/6

g = 4

Solution g = 4 and h = 2