Question

Consider the system of linear equations. 5 x + 10 y = 15. 10 x + 3 y = 13 To use the linear combination method and addition to eliminate the x-terms, by which number should the first equation be multiplied? –2 Negative one-half One-half 2

Answer 1

• Answer:

Solve the following system:

5 x + 10 y = 15 | (equation 1)

10 x + 3 y = 13 | (equation 2)

Swap equation 1 with equation 2:

{10 x + 3 y = 13 | (equation 1)

5 x + 10 y = 15 | (equation 2)

Subtract 1/2 × (equation 1) from equation 2:

{10 x + 3 y = 13 | (equation 1)

0 x+(17 y)/2 = 17/2 | (equation 2)

Multiply equation 2 by 2/17:

{10 x + 3 y = 13 | (equation 1)

0 x+y = 1 | (equation 2)

Subtract 3 × (equation 2) from equation 1:

{10 x+0 y = 10 | (equation 1)

0 x+y = 1 | (equation 2)

Divide equation 1 by 10:

{x+0 y = 1 | (equation 1)

0 x+y = 1 | (equation 2){

• Collect results:

Answer: x = 1/2

Answer 2

Answer:

Solve the following system:

{5 x + 10 y = 15 | (equation 1)

10 x + 3 y = 13 | (equation 2)

Swap equation 1 with equation 2:

{10 x + 3 y = 13 | (equation 1)

5 x + 10 y = 15 | (equation 2)

Subtract 1/2 × (equation 1) from equation 2:

{10 x + 3 y = 13 | (equation 1)

0 x+(17 y)/2 = 17/2 | (equation 2)

Multiply equation 2 by 2/17:

{10 x + 3 y = 13 | (equation 1)

0 x+y = 1 | (equation 2)

Subtract 3 × (equation 2) from equation 1:

{10 x+0 y = 10 | (equation 1)

0 x+y = 1 | (equation 2)

Divide equation 1 by 10:

{x+0 y = 1 | (equation 1)

0 x+y = 1 | (equation 2)

Collect results:

Answer: x = 1, y = 1