Can someone explain how to solve this system using substitution?
1.25x + 0.75y = 109.75
x + y = 105
sure. the 2nd equation says that
y = 105-x.
Substitute that into the first equation to get
1.25x + 0.75(105-x) = 109.75
x = 62
So, y = 105-62 = 43
1.25x + 0.75y = 109.75
x + y = 105 > x = 105 - y
Put x value in the first equation;
1.25(105 - y) + 0.75y = 109.75
131.25 - 1.25y + 0.75y = 109.75
131.25 - 0.5y = 109.75
-131.25 -131.25
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-0.5y = -21.5
______ _______
-0.5 -0.5
y = 43
Now solve for x. Use either equation.
x = 105 - 43
x = 62
x = 62
To solve this system of equations using substitution, follow the steps below:
Step 1: Solve one equation for one variable in terms of the other variable.
In this case, let's solve the second equation (x + y = 105) for x.
x = 105 - y
Step 2: Substitute the expression for x from Step 1 into the other equation.
Replace x in the first equation (1.25x + 0.75y = 109.75) with (105 - y).
1.25(105 - y) + 0.75y = 109.75
Step 3: Simplify and solve the resulting equation.
Multiply 1.25 by each term inside the parentheses:
(1.25 * 105) - (1.25 * y) + 0.75y = 109.75
131.25 - 1.25y + 0.75y = 109.75
Combine like terms:
(0.75y - 1.25y) + 131.25 = 109.75
-0.5y + 131.25 = 109.75
Subtract 131.25 from both sides:
-0.5y = -21.5
Step 4: Solve for y.
Divide both sides by -0.5:
y = -21.5 / -0.5
y = 43
Step 5: Substitute the value of y back into one of the original equations to solve for x.
Using equation x + y = 105:
x + 43 = 105
Subtract 43 from both sides:
x = 105 - 43
x = 62
So, the solution to the system of equations using substitution is x = 62 and y = 43.
To solve this system using substitution, we will solve one of the equations for one variable and substitute that expression into the other equation.
Let's start with the second equation:
x + y = 105
From this equation, we can solve for x:
x = 105 - y
Now we substitute this expression for x in the first equation:
1.25x + 0.75y = 109.75
Replacing x with the expression we found:
1.25(105 - y) + 0.75y = 109.75
Now we can simplify and solve for y:
131.25 - 1.25y + 0.75y = 109.75
Combining like terms:
0.5y = -21.5
Dividing both sides by 0.5:
y = -21.5 / 0.5
y = -43
Now plug this value back into either equation to solve for x:
x + (-43) = 105
x - 43 = 105
Adding 43 to both sides:
x = 148
So the solution to the system of equations is x = 148 and y = -43.