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.
We have been given the following system of equations.
2y+x=- 4 & (I) y-x=- 5 & (II)
Let's start by isolating the y variable in Equation (II).
y-x=- 5 ⇔ y=- 5+x
Now we can substitute (II) into (I) and solve for x.
2y+x=- 4 & (I) y=- 5+x & (II)
2( - 5+x)+x=- 4 y=- 5+x
- 10+2x+x=- 4 y=- 5+x
- 10+3x=- 4 y=- 5+x
3x=6 y=- 5+x
x=2 y=- 5+x
Now, to find the value of y, we need to substitute x=2 into either one of the equations in the given system. Let's use the second equation.
x=2 y=- 5+x
x=2 y=- 5+ 2
x=2 y=- 3
The solution, or , to this system of equations is the point (2,- 3).
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.
2y+x=- 4 & (I) y-x=- 5 & (II)
2( - 3)+ 2? =- 4 - 3- 2? =- 5
- 6+2? =- 4 - 3-2? =- 5
(I), (II):Add and subtract terms
- 4=- 4 ✓ - 5=- 5 ✓
Because both equations are true statements, we know that our solution is correct.
