Solve the system by substitution:
-4.5x-2y=-12.15
3.25x-y=-0.75
To solve the system of equations using substitution, we will solve one equation for one variable and then substitute that expression into the other equation.
Let's solve the second equation for y:
3.25x - y = -0.75
Step 1: Add y to both sides of the equation:
3.25x = y - 0.75
Step 2: Add 0.75 to both sides of the equation:
3.25x + 0.75 = y
Now, we have y expressed in terms of x. We will substitute this expression for y in the first equation:
-4.5x - 2y = -12.15
Step 1: Substitute y with 3.25x + 0.75:
-4.5x - 2(3.25x + 0.75) = -12.15
Step 2: Distribute -2 to both terms inside the parentheses:
-4.5x - 6.5x - 1.5 = -12.15
Step 3: Combine like terms:
-11.0x - 1.5 = -12.15
Step 4: Add 1.5 to both sides of the equation:
-11.0x = -10.65
Step 5: Divide both sides of the equation by -11.0 to solve for x:
x = (-10.65) / (-11.0)
x ≈ 0.9682
Now we substitute the value of x into the expression we found for y:
y = 3.25x + 0.75
y = 3.25(0.9682) + 0.75
y ≈ 3.1497
Therefore, the solution to the system of equations is x ≈ 0.9682 and y ≈ 3.1497.
-4.5 x - 2 y = -12.15
3.25 x - 1 y = -0.75 mult by 2
-4.5 x - 2 y = -12.15
6.50 x - 2 y = -1.50
---------------------subtract
-11 x + 0 = -10.65
so
x = 10.65/11 etc