Use substitution to solve the system

3x + 7y = −3 (1)
7x + y = −53 (2)
Find the value of x.

(part 2 of 2)Find the value of y.

for (2)

y = -7x - 53

sub into (1)
3x + 7(-7x-53) = -3
3x - 49x - 371 = -3
-46x = 368
x = -8

sub that back into y = .... to get y

To solve the system of equations using the method of substitution, we need to solve one equation for one variable and then substitute that expression into the other equation. Let's solve equation (2) for y and substitute it into equation (1) to find the value of x.

Step 1: Solve equation (2) for y:
Start with equation (2): 7x + y = -53
Subtract 7x from both sides: y = -7x - 53

Step 2: Substitute y in equation (1) with the expression -7x - 53:
Substitute -7x - 53 for y in equation (1): 3x + 7(-7x - 53) = -3

Now we can solve this equation for x:

Step 3: Distribute the 7 to -7x and -53:
3x - 49x - 371 = -3

Step 4: Combine like terms:
-46x - 371 = -3

Step 5: Add 371 to both sides to isolate the variable term:
-46x = 368

Step 6: Divide both sides by -46 to solve for x:
x = 368/-46
x = -8

Now that we have the value of x, we can substitute it back into y = -7x - 53 to find the value of y.

Step 7: Substitute x = -8 into y = -7x - 53:
y = -7(-8) - 53
y = 56 - 53
y = 3

Therefore, the value of x is -8 and the value of y is 3.