Answer
To solve the system of equations using the substitution method, you can follow these steps:
Given equations:
1. 10x - 2y = 16
2. 5x + 3y = -12
Step 1: Solve one of the equations for one variable. Let's solve equation (1) for x:
10x - 2y = 16
First, add 2y to both sides:
10x = 2y + 16
Next, divide both sides by 10 to isolate x:
x = (2y + 16) / 10
x = (y + 8) / 5
Step 2: Substitute the expression you found for x (from step 1) into the other equation (equation 2):
5x + 3y = -12
Replace x with (y + 8) / 5:
5((y + 8) / 5) + 3y = -12
Now, simplify the equation:
(y + 8) + 3y = -12
Step 3: Solve the equation for y:
Combine like terms:
4y + 8 = -12
Subtract 8 from both sides:
4y = -12 - 8
4y = -20
Divide by 4 to isolate y:
y = -20 / 4
y = -5
Step 4: Now that you have found the value of y, substitute it back into the expression for x that you found in step 1:
x = (y + 8) / 5
x = (-5 + 8) / 5
x = 3 / 5
So, the solution to the system of equations is:
x = 3/5
y = -5