I need help solving the linear system using substitution of the below problem....Thank You
3x - y=2
y= 2x - 9
3x-2x-9=2
x = 11
y=2*11-9
y=22-9
y=13
To solve the given linear system using substitution, we can substitute the value of y from the second equation into the first equation. Let's start step by step:
Step 1: Given equations:
1) 3x - y = 2
2) y = 2x - 9
Step 2: Substitute the value of y from equation 2 into equation 1.
3x - (2x - 9) = 2
Step 3: Simplify the equation by distributing the negative sign.
3x - 2x + 9 = 2
Step 4: Combine the like terms and simplify further.
x + 9 = 2
Step 5: Isolate the variable x by subtracting 9 from both sides of the equation.
x = 2 - 9
x = -7
Step 6: Now substitute the value of x into equation 2 to find the value of y.
y = 2(-7) - 9
y = -14 - 9
y = -23
Step 7: The solution to the linear system is x = -7 and y = -23.
Thus, the solution to the given linear system using substitution is x = -7 and y = -23.
To solve the linear system using substitution, follow these steps:
1. Start with the given equations:
3x - y = 2 ...(equation 1)
y = 2x - 9 ...(equation 2)
2. Solve one of the equations for one variable in terms of the other. In this case, equation 2 is already solved for y in terms of x.
3. Substitute the expression for the variable from step 2 into the other equation. In this case, substitute y = 2x - 9 into equation 1:
3x - (2x - 9) = 2
4. Simplify and solve the resulting equation:
3x - 2x + 9 = 2
x + 9 = 2
x = 2 - 9
x = -7
5. Substituting the value of x back into equation 2 to find the value of y:
y = 2(-7) - 9
y = -14 - 9
y = -23
Therefore, the solution to the linear system is x = -7 and y = -23.