Question

Determine the number of solutions for this system of equations by inspection only. Explain. 7x+6y = 19 56x+48y = 106 Question content area bottom Part 1 Select the correct answer below and fill in the answer box to complete your choice. A. There is one solution. If the first equation is multiplied by enter your response here​, the​ x-terms will be the same but the​ y-terms will not.​ So, the​ x-term will be eliminated leaving a​ y-term and a constant. B. There are infinitely many solutions. If the first equation is multiplied by enter your response here​, the like variable terms and constants will be the same.​ So, each term will be eliminated. This results in the statement 0=​0, which is true. C. There is no solution. If the first equation is multiplied by enter your response here​, the like v

Answer 1

In this case, the system of equations is: 7x + 6y = 19 and 56x + 48y = 106.

By multiplying the first equation by 8 and the second equation by 1, we can eliminate the x-term and determine that there is one solution for this system of equations.

Therefore, the correct answer is: option A.) There is one solution. If the first equation is multiplied by enter your response here​, the​ x-terms will be the same but the​ y-terms will not.​ So, the​ x-term will be eliminated leaving a​ y-term and a constant.

Step-by-step explanation:

To determine the number of solutions for a system of equations by inspection, we need to look at the coefficients of the x and y terms in each equation. In this case, the system of equations is:

7x + 6y = 19

56x + 48y = 106

By inspecting the coefficients, we can see that if we multiply the first equation by 8 and the second equation by 1, the x-terms will be the same but the y-terms will not.

This means that the x-term will be eliminated when we subtract the equations, leaving only a y-term and a constant.

Therefore, there is one solution for this system of equations.