finding the answer using Elimination!!!!!!!!!!!!!!!!!!!!!!!!!!!
In elimination, the easiest way to solve it is by multiplying one or both equations until two of the variables form a direct opposite of each other. Since we already know the two equations we are going to use (1.5x+0.5y=78.50 and x+y=87), we can start multiplying the equations.
Step-by-Step Procedures:
1.5x+0.5y=78.50
x+y=87
Multiply the two equations Until Obtained a Direct Opposite!!!!!!!!!!!!!!!!!!!!!!!!!
Since the y-variable for the first equation can be multiplied into the y-variable of the second equation, we can just multiply it by however much it needs to be multiplied to fit in the second y-variable, and continue with the next step. Don't FORGET to multiply both sides of the equation to keep it even!!!!!!!!!!!!!!
(-2)(1.5x+0.5y)=78.50(-2)
x+y=87
=====================
-3x-y=-157
x+y=87
Add the two equations together to solve one variable!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
-3x-y=157
x+y=87
(The -y and y cancels out leaving only ONE variable!!!!!!!!!)
-2x=-70
x=35
Substitute the x-value for y and solve the rest of the equation!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
x=35
x+y=87
35+y=87
35-35+y=87-35
y=52
Check your answers!!!!!!!!!!!!!!!!!!!!!!!!!!!!
1.5x+50y=78.5
1.5(35)+50(35)=78.5
52.5+26=78.5
and....
x+y=87
35+52=87.
Step-by-Step Procedures:
1.5x+0.5y=78.50
x+y=87
Multiply the two equations Until Obtained a Direct Opposite!!!!!!!!!!!!!!!!!!!!!!!!!
Since the y-variable for the first equation can be multiplied into the y-variable of the second equation, we can just multiply it by however much it needs to be multiplied to fit in the second y-variable, and continue with the next step. Don't FORGET to multiply both sides of the equation to keep it even!!!!!!!!!!!!!!
(-2)(1.5x+0.5y)=78.50(-2)
x+y=87
=====================
-3x-y=-157
x+y=87
Add the two equations together to solve one variable!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
-3x-y=157
x+y=87
(The -y and y cancels out leaving only ONE variable!!!!!!!!!)
-2x=-70
x=35
Substitute the x-value for y and solve the rest of the equation!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
x=35
x+y=87
35+y=87
35-35+y=87-35
y=52
Check your answers!!!!!!!!!!!!!!!!!!!!!!!!!!!!
1.5x+50y=78.5
1.5(35)+50(35)=78.5
52.5+26=78.5
and....
x+y=87
35+52=87.