I need help, i have to solve the linear solution using substitution, the equations are 4x+3=y and x=y-2
Also, please show me how you did it if possible.
Thanks!
To solve the system of equations using substitution, we need to find the value of one variable and substitute it into the other equation.
Let's start with the second equation: x = y - 2.
We can now substitute this expression for x into the first equation: 4x + 3 = y.
Substituting x = y - 2, we get 4(y - 2) + 3 = y.
Now, let's simplify the equation: 4y - 8 + 3 = y.
We combine like terms: 4y - 5 = y.
Next, we want to isolate the variable y. To do this, we can subtract y from both sides: 4y - y - 5 = 0.
Simplifying further, we have: 3y - 5 = 0.
Now, let's solve for y. Adding 5 to both sides of the equation gives us: 3y = 5.
Finally, divide both sides of the equation by 3 to solve for y: y = 5/3 ≈ 1.667.
Now that we have the value of y, we can substitute it back into one of the original equations to find the value of x. Using the second equation x = y - 2, when y = 5/3, we get x = 5/3 - 2 = -1/3 ≈ -0.333.
So the solution to the system of equations is x ≈ -0.333 and y ≈ 1.667.
By following the steps above, you should be able to solve any system of linear equations using the substitution method.