Solve the system by substitution:
-4.5x-2y=-12.15
3.25x-y=-0.75
y = 3.25x - .75
-4.5x - 2y = -4.5x - 2(3.25x-.75) = 12.15
Solve for x, then y. To check, put both values into your first equation in your question above.
To solve the system of equations by substitution, we will solve one equation for one variable and then substitute that expression into the other equation. Let's choose the second equation to solve for y.
First, we rearrange the second equation:
3.25x - y = -0.75
Adding y to both sides gives:
3.25x = y - 0.75
Now, we have isolated y in terms of x. We can substitute this expression for y in the first equation:
-4.5x - 2(y) = -12.15
Substituting y:
-4.5x - 2(3.25x - 0.75) = -12.15
Simplifying, we distribute the 2:
-4.5x - 6.5x + 1.5 = -12.15
Combining like terms on the left side:
-11x + 1.5 = -12.15
Next, we can subtract 1.5 from both sides:
-11x = -13.65
Finally, divide both sides by -11 to solve for x:
x = (-13.65) / (-11)
x ≈ 1.24
Now that we have found the value of x, we can substitute it back into one of the original equations to solve for y. Let's use the second equation:
3.25x - y = -0.75
Substituting x ≈ 1.24:
3.25(1.24) - y = -0.75
Simplifying:
4.03 - y = -0.75
Next, we subtract 4.03 from both sides:
-y = -4.78
Multiplying by -1 to solve for y:
y ≈ 4.78
So the solution to the system of equations is x ≈ 1.24 and y ≈ 4.78.