Solve the system by substitution
{-4.5x-2y=-12.5
3:25x-y=-0.75}
that last equation should have been
13x - 4y = -3
I would first of all eliminate those decimals
-4.5x-2y=-12.5
times 2 ------> -9x - 4y = -25 or 9x + 4y = 25
3.25x-y=-0.75
times 4 -------> 13x - 4y = 3
now just add them and things will work out
To solve the system of equations by substitution, we can solve one equation for one variable in terms of the other variable and then substitute that expression into the other equation.
Let's solve the second equation for y:
3.25x - y = -0.75
Adding y to both sides and rearranging, we get:
y = 3.25x + 0.75
Now we substitute this expression for y in the first equation:
-4.5x - 2(3.25x + 0.75) = -12.5
Simplifying, we have:
-4.5x - 6.5x - 1.5 = -12.5
Combining like terms:
-11.0x - 1.5 = -12.5
Adding 1.5 to both sides:
-11.0x = -11.0
Finally, dividing both sides by -11, we find:
x = 1.0
Now, substitute this value of x back into the second equation to find the value of y:
3.25(1.0) - y = -0.75
3.25 - y = -0.75
Subtracting 3.25 from both sides:
-y = -4.00
Multiplying both sides by -1:
y = 4.00
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'll solve one of the equations for one variable and substitute it into the other equation. Let's solve the second equation for y.
First, we have the equations:
1) -4.5x - 2y = -12.5
2) 3.25x - y = -0.75
Let's solve the second equation, equation 2, for y:
2) 3.25x - y = -0.75
Add y to both sides:
3.25x = y - 0.75
Add 0.75 to both sides:
3.25x + 0.75 = y
Now we have an expression for y in terms of x: y = 3.25x + 0.75
Next, we'll substitute this expression for y into the first equation, equation 1:
-4.5x - 2y = -12.5
Replace y with 3.25x + 0.75:
-4.5x - 2(3.25x + 0.75) = -12.5
Expand the parentheses:
-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 = -12.5 + 1.5
-11.0x = -11.0
Divide both sides by -11.0:
x = -11.0 / -11.0
Simplify:
x = 1.0
Now, substitute the value of x back into the expression for y:
y = 3.25x + 0.75
y = 3.25(1.0) + 0.75
y = 3.25 + 0.75
y = 4.0
Therefore, the solution to the system of equations is x = 1.0 and y = 4.0.