Question

Please help me with this problem so I can help my son better understand this problem. I have attached an image of what were working on. Which properties justify the steps taken to solve the system?{4x+3y=25 2x+−5y=19}Drag the answers into the boxes to match each step.Addition property of equalitySubtraction property equalitySubstitution property of equalityMultiplication property of equality 4x+3y=25; −4x+10y=−38 13y=−13y=−14x+3(−1)=254x−3=254x = 28x = 7

Answer 1

Given equations,

`\begin{gathered} 4x+3y=25\ldots\ldots(1) \\ 2x\pm5y=19\ldots\ldots.(2) \end{gathered}`

Step 1) In step 1, multiply the second equation by -2.

Thus, the multiplication property of equality.

Step 2) In step 2, we add both equations generated in step 1.

Thus, the additional property of equality.

Step 3) We divide both sides of the equation obtained in step 2 by 13.

Thus, the division property of equality.

Step 4) We substitute the value obtained in step 3 for y in the first equation.

Thus, the substitution property of equality.

Step 5) Simplify.

Step 6) We add +3 on both sides of the equation in order to have an equation with a variable x.

Thus, the additional property of equality.

Step 7) We divide both sides of the equation obtained to get the value of x.

Thus, division property of equality.