When solving a using , there are three steps.
- Isolate a in one of the .
- Substitute the expression for that variable into the other equation and solve.
- Substitute this solution into one of the equations and solve for the value of the other variable.
For this exercise, y is already isolated in one equation, so we can skip straight to step 2!
y=x-4 & (I) -2x+y=18 & (II)
y=x-4 -2x+ x-4=18
y=x-4 - x-4=18
y=x-4 - x=22
y=x-4 x=-22
Now, to find the value of y, we need to substitute x=-22 into either one of the equations in the given system. Let's use the first equation.
y=x-4 x=-22
y= -22-4 x=-22
y=-26 x=-22
The solution, or , to this system of equations is the point (-22,-26).
Checking Our Solution
To check our answer, we will substitute our solution into both equations. If doing so results in true statements, then our solution is correct.
y=x-4 & (I) -2x+y=18 & (II)
(I), (II): x= -22, y= -26
-26? = -22-4 -2( -22)+( -26)? =18
-26? =-22-4 44+(- 26)? =18
-26? =-22-4 44-26? =18
(I), (II): Subtract terms
-26=-26 18=18
Because both equations are true statements, we know that our solution is correct.
