use method of substitution to solve the system of linear equation
3x+4y=3/2 y=2x-1
so, substitute:
y = 2x-1
3x + 4(2x-1) = 3/2
11x - 4 = 3/2
11x = 11/2
x = 1/2
so, y=2x-1 = 0
To solve the system of linear equations using the method of substitution, follow these steps:
Step 1: Choose one equation and solve for one variable in terms of the other variable.
Let's choose the second equation, which is y = 2x - 1.
Step 2: Substitute the expression from step 1 into the other equation.
We substitute y = 2x - 1 into the first equation: 3x + 4(2x - 1) = 3/2.
Step 3: Simplify and solve for the remaining variable.
Expanding and simplifying the equation, we get: 3x + 8x - 4 = 3/2.
Combine like terms: 11x - 4 = 3/2.
Add 4 to both sides of the equation: 11x = 3/2 + 4.
11x = 3/2 + 8/2 = 11/2.
Divide both sides by 11: x = (11/2) / 11.
x = 1/2.
Step 4: Substitute the value of x into one of the original equations to solve for the other variable.
Let's substitute x = 1/2 into the second equation: y = 2(1/2) - 1.
y = 1 - 1.
y = 0.
Step 5: Check the solution.
Now, substitute the values of x and y into the original equations to verify if they satisfy both equations.
For the first equation: 3(1/2) + 4(0) = 3/2.
3/2 = 3/2. This equation holds true.
For the second equation: 0 = 2(1/2) - 1.
0 = 1 - 1.
0 = 0. This equation also holds true.
Therefore, the solution to the system of linear equations is x = 1/2 and y = 0.