Answer:
1. x = 0, y = 6
2. x = 2, y = -2
3. no solution
4. x = 1 - y
Explanation:
To solve by substitution, you just pick one of the two equations and solve for one of the variables. It doesn't matter which one, but I would suggest doing whatever is easiest.
Let's do it!
Example 1:
x + 5 = 5
2x + y = 6
let's solve the first equation and substitute it into the second equation
x + 5 = 5
combine like terms
x = 5 - 5
x = 0
Now we plug in 0 for x in the second equation to solve for y
2(0) + y = 6
0 + y = 6
y = 6- 0
y = 6
Final answer: x = 0, y = 6
Example 2:
2x + y = 2
2x - y = 6
let's solve Equation 1
2x + y = 2
y = 2 - 2x
Now we plug in 2 - 2x in the second equation for y
2x - y = 6
2x - (2 - 2x) = 6
4x - 2 = 6
4x = 6 + 2
4x = 8
x = 2
But we are not done yet! We don't know the exact value for y, so we are gonna take our x = 2 and plug it into the y equation
y = 2 - 2x
y = 2 - 2(2)
y = 2 - 4
y = -2
Final answer: x = 2, y = -2
Example 3:
2x + y =3
2x + y = 5
solving equation 1
y = 3 - 2x
plugging it in equation 2
2x + y = 5
2x + ( 3 - 2x ) = 5
0x + 3= 5
0x = 2x
NO SOLUTION, EXAMPLE 3 HAS NO SOLUTION AND CANNOT BE SOLVED
Example 4:
3x + 3y = 3
x + y = 1
Let's solve equation 2 instead of 1 first, because it looks easier
x + y = 1
x = 1 - y
Plug it in equation 1
3x + 3y = 3
3( 1 - y) + 3y = 3
3 - 3y + 3y = 3
3 - 0 = 3
3 = 3
This equation only has ONE SOLUTION
the solution is X = 1 - Y