Please solve the system with the elimination method. Explain each step as it is performed.

5y = x
2x - 3y = 7

Would the elimination method have been your first choice to solve this problem?

Elimination is a poor choice for this question.

I would definitely use substitution.

sub the 1st into the 2nd
2(5y) - 3y = 7
10y-3y=7
7y=7
y = 1 , then x = 5

compare this with elimination:

5y = x
x - 5y = 0
multiply by 2,
2x - 10y = 0
2x - 3y = 7
subtract them
-7y = -7
y = 1
sub into 1st:
5(1) = x
x = 5

To solve the given system of equations using the elimination method, let's go step by step:

Step 1: Multiply the first equation by 2 to make the coefficients of 'x' in both equations equal:
10y = 2x

Step 2: Rewrite the second equation:
2x - 3y = 7

Step 3: Multiply the second equation by 5 to make the coefficients of 'x' in both equations equal:
10x - 15y = 35

Now we have two equations with equal coefficients for 'x', allowing us to eliminate 'x' from the equations.

Step 4: Subtract the first equation from the second equation:
(10x - 15y) - (10y = 2x) = 35 - 0

Simplifying, we get:
10x - 15y - 10y - 2x = 35

Combining like terms, we have:
8x - 25y = 35

Step 5: Now we have a new equation:
8x - 25y = 35

This equation is in terms of 'x' and 'y' after the elimination of 'x'.

Step 6: Solve this equation for either 'x' or 'y' to find the value of one variable.

Step 7: Plug the value of the variable found in Step 6 back into one of the original equations to solve for the remaining variable.

Since only one equation was given to solve for 'x' or 'y', this system is not well-suited for the elimination method. The substitution method would be more appropriate to solve this system of equations.