x-2y=.9
4x-3y=13.1
Solve using the substitution method.
Well first you change x - 2y = .9 to x = .9 + 2y, by adding y from both sides of the equation.
Then, you substitute x=.9 + 27 into 4x - 3y = 13.1 to get 4(.9 + 2y)- 3y= 13.1. Use the distrubutive property and you get 4 * .9 = 3.6 and 4 * 2y = 8y.
Now you have 3.6 + 8y - 3y = 13.1. Simplify to get 3.6 + 5y = 13.1, since 8y - 3y = 5y.
So you subtract 3.6 from both sides to get 5y = 9.5. Divide this by -9 on both sides to get y = 1.9
Plug this in to one of the equations: x - 2y = .9 to get x - 2(1.9) = .9.
You get x - 3.8 = .9. Add 3.8 to both sides to get x=4.7.
The answer is (4.7 , 1.9)
To solve the system of equations using the substitution method, we will solve one equation for a variable and substitute it into the other equation.
Let's solve the first equation for x:
x - 2y = 0.9
x = 0.9 + 2y
Now, substitute the value of x in the second equation:
4(0.9 + 2y) - 3y = 13.1
Simplify and solve for y:
3.6 + 8y - 3y = 13.1
5y + 3.6 = 13.1
5y = 13.1 - 3.6
5y = 9.5
y = 9.5/5
y = 1.9
Now substitute the value of y into the first equation to solve for x:
x - 2(1.9) = 0.9
x - 3.8 = 0.9
x = 0.9 + 3.8
x = 4.7
Therefore, the solution to the system of equations is x = 4.7 and y = 1.9.
To solve the system of equations using the substitution method, follow these steps:
Step 1: Solve one equation for one variable.
Let's solve the first equation, x - 2y = 0.9, for x.
x = 0.9 + 2y
Step 2: Substitute the expression for that variable into the other equation.
Now, substitute x with 0.9 + 2y in the second equation:
4(0.9 + 2y) - 3y = 13.1
Step 3: Simplify the equation.
Expand the left side of the equation:
3.6 + 8y - 3y = 13.1
Combine like terms:
5y + 3.6 = 13.1
Step 4: Solve the equation for the remaining variable.
Subtract 3.6 from both sides of the equation:
5y = 13.1 - 3.6
5y = 9.5
Divide both sides by 5:
y = 9.5 / 5
y = 1.9
Step 5: Substitute the found value for y back into either of the original equations to find x.
Let's use the first equation, x - 2y = 0.9:
x - 2(1.9) = 0.9
x - 3.8 = 0.9
Add 3.8 to both sides of the equation:
x = 0.9 + 3.8
x = 4.7
So, the solution to the system of equations is x = 4.7 and y = 1.9.