Question

A system of linear equations is shown below. 2x+4y=103x−y=8 Maria is attempting to prove that by replacing 2x+4y=10 with a different equation it will sometimes produce a new system of equations with the same solution. Maria plans on multiplying 2x+4y=10 by 2 and then adding the results to the equation 3x−y=8 in order to create a new equation. Maria claims that the new equation that she will replace 2x+4y=10 with is 7x+7y=12. Is Maria correct? Why or why not?

Answer 1

No she is wrong.

Step-by-step explanation:

`\sf\\2x+4y=10...........(1)\\3x-y=8...........(2)\\\\\textsf{First Maria multiplies equation(1) by 2:}\\2(2x+4y)=2(10)\\\textsf{or, }4x+8y=20........(3)\\\\\textsf{Then she adds the resulting equation to equation (3):}\\(4x+8y)+(3x-y)=20+8\\\textsf{or, }7x+7y=28`

`\textsf{Maria is wrong because she obtained the wrong equation.}`