Question

Please help me with this problem:Which properties justify the steps taken to solve the system?{2x−4y=183x+3y=0Drag and drop the answers into the boxes to match each step. Image is attached

Answer 1

First step.

If we multiply by 3 the first equation and by 2 the second equation we get the first step:

$\begin{gathered} 6x-12y=54 \\ 6x+6y=0 \end{gathered}$

therefore, the answer for the first box is: Multiplication property of equality.

Second step.

If we subtract both equations, we have

$-18y=54$

then, the answer for the second box is: Subtraction property of equality

Third step.

By dividing both sides of our last result by -18, we get

$y=\frac{54}{-18}=-3$

then, the answer for the third step is: Division property of equality.

Fourth step.

Once we have obtained the result for variable y (which is -3), we need to find the result for variable x. So, by substituting our result for y into the first equation, we have

$2x-4(-3)=18$

Therefore, the answer for the fourth box is: Substitution property of equality.

Fifth step.

Then, by simplifying our last result, in which there is a product of -4 and -3, we get

$2x+12=18$

Thefore, the answer for the fifth box is: Simplify.

Sixth step.

Now, by subtracting 12 to both sides, we have

$2x=6$

then, the answer for the sixth box is: Subtraction property of equality.

Seventh step.

Finally, by dividing both sides by 2, we obtain

$x=3$

Then, the answer for the seventh box is: Division property of equality.