I'm working on solving linear systems by substitution, here are the equations:
4x+3=y and x=y-2
what is the sollution?
and please show me the steps! thanks!
To solve the linear system by substitution method, we'll follow these steps:
Step 1: Solve one of the equations for one variable.
Step 2: Substitute the expression from step 1 into the other equation.
Step 3: Solve the resulting equation.
Step 4: Substitute the solution found in step 3 into one of the original equations to find the value of the other variable.
Let's solve your system:
Given equations:
1) 4x + 3 = y
2) x = y - 2
Step 1: Solve equation (2) for x:
x = y - 2
Step 2: Substitute the value of x (from step 1) into equation (1):
4(y - 2) + 3 = y
Step 3: Simplify the equation obtained in step 2:
4y - 8 + 3 = y
4y - 5 = y
Step 4: Now, let's isolate y. Move the y term to one side of the equation:
4y - y = 5
3y = 5
Divide both sides of the equation by 3:
y = 5/3
Step 5: Substitute this value of y back into equation (2) to find x:
x = (5/3) - 2
x = (5/3) - (2*3/3)
x = (5 - 6)/3
x = -1/3
So, the solution to the system of equations is:
x = -1/3, and y = 5/3.
To solve this system of linear equations by substitution, we'll solve one equation for one variable and then substitute the value into the other equation. Here are the steps:
Step 1: Start with the first equation: 4x + 3 = y.
Step 2: Solve the second equation for x:
x = y - 2.
Step 3: Substitute the x-value from the second equation into the first equation:
4(y - 2) + 3 = y.
Step 4: Distribute the 4 on the left side:
4y - 8 + 3 = y.
Step 5: Combine like terms:
4y - 5 = y.
Step 6: Bring all the y-terms to one side:
4y - y = 5.
Step 7: Combine the y-terms:
3y = 5.
Step 8: Divide both sides by 3 to isolate y:
y = 5/3.
Step 9: Substitue the y-value back into the second equation to solve for x:
x = (5/3) - 2 = -1/3.
Therefore, the solution to the system of equations is x = -1/3 and y = 5/3.