Use the substitution method to solve the system 2.5x+y=−2 , 3x+2y=0 .
To solve the system of equations using the substitution method, we start with one equation and solve it for one variable in terms of the other. Then we substitute this expression into the other equation and solve for the remaining variable.
Let's start with the first equation:
2.5x + y = -2
Solving this equation for y, we can subtract 2.5x from both sides:
y = -2 - 2.5x
Now, we substitute this expression for y into the second equation:
3x + 2(-2 - 2.5x) = 0
Distribute the 2 to both terms inside the parentheses:
3x - 4 - 5x = 0
Combine like terms:
-2x - 4 = 0
Add 4 to both sides:
-2x = 4
Divide both sides by -2:
x = -2
Now that we have the value of x, we can substitute it back into the expression for y that we found earlier:
y = -2 - 2.5x
y = -2 - 2.5(-2)
y = -2 + 5
y = 3
Therefore, the solution to the system of equations is x = -2 and y = 3.