Enter your answer and show all the steps that you use to solve this problem in the space provided. Solve the system by substitution. {−4.5x−2y=−12.53.25x−y=−0.75
To solve the system by substitution, we'll solve one equation for one variable and substitute it into the other equation.
Let's solve the second equation for y.
3.25x - y = -0.75
First, let's isolate y by subtracting 3.25x from both sides:
-y = -3.25x - 0.75
Next, multiply each term by -1 to flip the sign:
y = 3.25x + 0.75
Now, we'll substitute this value of y into the first equation:
-4.5x - 2y = -12.5
Substituting y:
-4.5x - 2(3.25x + 0.75) = -12.5
Distribute the -2:
-4.5x - 6.5x - 1.5 = -12.5
Combine like terms:
-11.0x - 1.5 = -12.5
Add 1.5 to both sides:
-11.0x = -11.0
Divide by -11.0:
x = 1.0
Now that we have the value for x, we can substitute it back into one of the original equations to find y.
Let's use the second equation:
3.25x - y = -0.75
Substituting x = 1.0:
3.25(1.0) - y = -0.75
Simplifying:
3.25 - y = -0.75
Subtracting 3.25 from both sides:
-y = -4.0
Dividing by -1:
y = 4.0
Therefore, the solution to the system of equations is x = 1.0 and y = 4.0.
To solve the system of equations by substitution, we need to isolate one variable (either x or y) in one equation and substitute it into the other equation.
Let's solve the second equation for x:
3.25x - y = -0.75
Adding y to both sides, we get:
3.25x = y - 0.75
Dividing both sides by 3.25, we have:
x = (y - 0.75) / 3.25
Now we substitute this expression for x into the first equation:
-4.5x - 2y = -12.5
Substituting the value of x, we have:
-4.5((y - 0.75) / 3.25) - 2y = -12.5
Multiplying both sides by 3.25 to eliminate the denominators:
-4.5(y - 0.75) - 6.5y = -40.625
Expanding and simplifying:
-4.5y + 3.375 - 6.5y = -40.625
Combine like terms:
-11y + 3.375 = -40.625
Subtracting 3.375 from both sides:
-11y = -44
Dividing both sides by -11:
y = 4
Now we substitute this value of y back into the expression for x:
x = (4 - 0.75) / 3.25
x = 3.25 / 3.25
x = 1
Therefore, the solution to the system of equations is x = 1 and y = 4.
To solve the system of equations by substitution, we will solve one equation for one variable and substitute the expression into the other equation.
Step 1: Start with the first equation of the system:
-4.5x - 2y = -12.5
Step 2: Solve the first equation for one variable. Let's solve it for x:
-4.5x = -12.5 + 2y
Divide both sides by -4.5:
x = (-12.5 + 2y) / -4.5
Now we have an expression for x in terms of y.
Step 3: Substitute the expression for x into the second equation of the system:
3.25x - y = -0.75
Replacing x with (-12.5 + 2y) / -4.5, we get:
3.25((-12.5 + 2y) / -4.5) - y = -0.75
Step 4: Simplify and solve for y. Multiply both sides of the equation by -4.5 to eliminate the fraction:
3.25(-12.5 + 2y) - 4.5y = -0.75( -4.5)
-40.625 + 6.5y - 4.5y = 0.75 * 4.5
-40.625 + 2y = 3.375
Step 5: Continue solving for y. Move -40.625 to the right side:
2y = 3.375 + 40.625
2y = 44
Step 6: Solve for y by dividing both sides by 2:
y = 44 / 2
y = 22
We have found the value of y as 22.
Step 7: Substitute the value of y back into the earlier expression for x:
x = (-12.5 + 2(22)) / -4.5
x = (-12.5 + 44) / -4.5
x = 31.5 / -4.5
x = -7
So the solution to the system of equations is x = -7 and y = 22.