Answer: One solution : [tex](5,3)[/tex] or [tex]x=5,y=3[/tex]
Step-by-step explanation:
Solving using the addition method means that we must eliminate variable with opposite signs to solve for the other one. Notice that the y-values have opposite signs(6 and -7 respectively). In some cases(this one), we will need to multiply both the top and bottom equations by a constant in order to solve.
Solving:
Given : [tex]3x+6y=33, 10x-7y=29[/tex]
Top Equation(multiply by 7) : [tex]7(3x+6y)=7(33)[/tex] → [tex]21x+42y = 231[/tex]
Bottom Equation(multiply by 6): [tex]6(10x-7y) = 6(29)[/tex] → [tex]60x-42y=174[/tex]
Now add the equations together(addition method):
[tex]21x+42y = 231[/tex]
[tex]60x-42y=174[/tex]
----------------------
[tex]81x=405[/tex]
--- ------ (Divide both sides by 81 to get x-value)
[tex]81[/tex] [tex]81[/tex]
[tex]x=5[/tex]
Now that we have x, plug it into the first equation and solve for y:
[tex]3(5)+6y=33[/tex]
[tex]6y+15=33[/tex]
[tex]6y=18[/tex]
[tex]y=3[/tex]
That's it!
