Question

Which properties justify the steps taken to solve the system? {3x-2y=10 4x-3y=14 drag and drop the answers into the boxes to match each step. put responses in the correct input to answer the question. select a response, navigate to the desired input and insert the response. responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. responses can also be moved by dragging with a mouse. {9x-6y=308x-6y=28 x = 2 3(2)-2y=10 6-2y=10 -2y=4 y=-2

Answer 1

The solution to the system of linear equations {3x - 2y = 10, 4x - 3y = 14} is x = 2, y = -2, found by first multiplying equations to equalize the coefficients of y, then subtracting them to solve for x, and substituting x back into an original equation to solve for y.

Step-by-step explanation:

The student is solving a system of linear equations using the method of substitution or elimination. To solve the system {3x - 2y = 10, 4x - 3y = 14}, one might multiply the entire first equation by 3, and the second by 2, to create a new system where the coefficients in front of y are equal but opposite. This results in:

• 9x - 6y = 30 (first equation multiplied by 3)
• 8x - 6y = 28 (second equation multiplied by 2)

Next, we can subtract the second equation from the first to eliminate y and find x:

• x = (30 - 28) / (9 - 8) = 2

Now we can substitute x = 2 back into either original equation to solve for y;

1. 3(2) - 2y = 10
2. 6 - 2y = 10
3. -2y = 4 (subtracting 6 from both sides)
4. y = -2 (dividing by -2)

Thus, the solution to the system of equations is x = 2, y = -2.