Question

To eliminate the x-terms and solve for y in the fewest steps, by which constants should the equations be multiplied? First equation: 6x − 5y = 17 Second equation: 7x + 3y = 11

Answer 1

To solve the system by eliminating the x-terms, multiply the first equation by 7 and the second by 6. Subtract the second resulting equation from the first to find that y = -1. Check the solution by substituting back into the original equations.

Step-by-step explanation:

To eliminate the x-terms and solve for y, we need to multiply the equations by constants that will allow the coefficients of x to be the same, but with opposite signs, so they cancel out when the equations are added together. For the first equation 6x - 5y = 17, and the second equation 7x + 3y = 11, we can multiply the first equation by 7 and the second equation by 6.

This leads to:

• First equation (multiplied by 7): 42x - 35y = 119
• Second equation (multiplied by 6): 42x + 18y = 66

Now, if we subtract the second equation from the first one, we get:

42x - 35y - (42x + 18y) = 119 - 66

This simplifies to:

• -53y = 53

Dividing both sides by -53:

• y = -1

With y = -1, we can then substitute this back into either of the original equations to solve for x. The goal of this process is to use systems of equations to eliminate terms and simplify the algebra. After finding a solution, it is always good practice to check the answer to ensure it is reasonable.

Answer 2

Step-by-step explanation:

The two equations we have are

6x − 5y = 17

7x + 3y = 11

Now to eliminate any term from them , we try to make the coefficient same . Here we want to eliminate the x term so it is important to make the coefficient of the x term same.

Lets multiply equation one by 7 and second equation by -6

6x − 5y = 17 )*7 => 42x-30y =119

7x + 3y = 11 ) *-6 +> -42x-18y= -66

Now coefficeint of x are same with opposite sign , so we need to multiply first equation by 7 and second by -6.