Solve the system by substitution.
-2.5x + y = 13.5
2.25x - y = -12.25
We can solve the system by substituting y in terms of x from the first equation into the second equation.
From the first equation, we have y = -2.5x + 13.5.
Substituting this into the second equation, we get:
2.25x - (-2.5x + 13.5) = -12.25
Simplifying, we get:
2.25x + 2.5x - 13.5 = -12.25
Combine like terms:
4.75x - 13.5 = -12.25
Add 13.5 to both sides:
4.75x = 1.25
Divide both sides by 4.75:
x = 1.25 / 4.75 = 0.263
Now substitute this value of x into either of the original equations to find y.
Using the first equation:
-2.5(0.263) + y = 13.5
-0.658 + y = 13.5
y = 14.158
Therefore, the solution to the system of equations is x = 0.263 and y = 14.158.
The given system of equations is:
-2.5x + y = 13.5 ---(1)
2.25x - y = -12.25 ---(2)
We will solve this system by using the method of substitution. Let's solve equation (2) for y and substitute it into equation (1).
From equation (2), we have:
2.25x - y = -12.25
Rearranging this equation, we get:
y = 2.25x + 12.25
Now, substitute this value of y into equation (1):
-2.5x + (2.25x + 12.25) = 13.5
Simplifying:
-2.5x + 2.25x + 12.25 = 13.5
-0.25x + 12.25 = 13.5
Subtracting 12.25 from both sides:
-0.25x = 13.5 - 12.25
-0.25x = 1.25
Dividing by -0.25:
x = 1.25 / -0.25
x = -5
Now, substitute this value of x back into equation (2) to find the value of y:
2.25(-5) - y = -12.25
Simplifying:
-11.25 - y = -12.25
Adding 11.25 to both sides:
-y = -12.25 + 11.25
-y = -1
Multiplying by -1:
y = 1
Therefore, the solution to the system of equations is x = -5 and y = 1.
To solve the system of equations by substitution, we need to isolate one variable in one of the equations and substitute it into the other equation.
Let's solve the first equation, -2.5x + y = 13.5, for y:
y = 2.5x + 13.5
Now we can substitute this expression for y into the second equation:
2.25x - (2.5x + 13.5) = -12.25
To simplify the equation, let's distribute the negative sign:
2.25x - 2.5x - 13.5 = -12.25
Combining like terms, we get:
-0.25x - 13.5 = -12.25
Next, let's isolate the x term by adding 13.5 to both sides of the equation:
-0.25x = -12.25 + 13.5
Simplifying, we have:
-0.25x = 1.25
To solve for x, divide both sides of the equation by -0.25:
x = 1.25 / -0.25
This gives us:
x = -5
Now that we know x, we can substitute it back into one of the original equations to find the value of y. Let's use the first equation:
-2.5(-5) + y = 13.5
Simplifying, we have:
12.5 + y = 13.5
Next, isolate y by subtracting 12.5 from both sides of the equation:
y = 13.5 - 12.5
This gives us:
y = 1
Therefore, the solution to the system of equations is x = -5 and y = 1.