Answer:
As you have written the equations, the solution is (-1.5, 1.5).
Step-by-step explanation:
As written, the system of equations is
[tex]\left \{ {{3y=x+6} \atop {y-x=3}} \right.[/tex]
To solve this, we will use substitution. First we will isolate y in the second equation:
y-x = 3
Add x to each side:
y-x+x = 3+x
y = 3+x
Now we will substitute this into the first equation
3y = x+6
3(3+x) = x+6
Using the distributive property,
3(3)+3(x) = x+6
9+3x = x+6
Subtract x from each side:
9+3x-x = x+6-x
9+2x = 6
Subtract 9 from each side:
9+2x-9 = 6-9
2x = -3
Divide both sides by 2:
2x/2 = -3/2
x = -1.5
Substitute this into the second equation:
y-(-1.5) = 3
y+1.5 = 3
Subtract 1.5 from each side:
y+1.5-1.5 = 3-1.5
y = 1.5
