how do i solve systems?
example- y=x-2 y=4x+1
set y = y
4x + 1 = x - 2
you finish it.
Multiple the first equation by -1:
-y=-x+2
Add it from the second one to get:
y=4x+1 +(-y=x+2)= 0=3x+3
Subtract 3 from both sides:
-3=3x
Divide by 3
x=-1
Plug it in for one equation:
y=(-1)-2
y=-3
To solve a system of equations, such as the example you provided, you can use one of the following methods:
1. Substitution Method:
Step 1: Begin by solving one of the equations for one variable (in this example, solve the first equation for y).
y = x - 2
Step 2: Substitute the expression of the variable (y) from the first equation into the second equation.
4x + 1 = x - 2
Step 3: Now, you have a single equation with one variable (x). Solve this equation for x.
4x - x = -2 - 1
3x = -3
x = -1
Step 4: Substitute the obtained value of x back into any of the original equations to find the corresponding value of y.
y = -1 - 2
y = -3
Therefore, the solution to the system of equations is x = -1 and y = -3.
2. Elimination Method:
Step 1: Align the two equations so that the coefficients of one of the variables (either x or y) are the same or multiples of each other.
In this example, let's multiply the first equation by 4 to give us:
4y = 4x - 8
Step 2: Subtract the modified equation from the second equation to eliminate one variable.
(4x + 1) - (4x - 8) = 0
-7 = 0
Step 3: Since -7 is not equal to 0, this implies that the system of equations is inconsistent, meaning there is no solution.
In this case, by applying the elimination method, we found that the system of equations has no solution.