our given system of equations is:
(please use Substitution)
3x+2y=44
6x−6y=18
Solve please with solutions
Answers
⇒Solutions
Substitution is the second method for solving a system of equations question. In order to solve this way, we must isolate one variable in one of the equations and then use that found variable for the second equation in order to solve for the remaining variable.
This may sound tricky, so let's look at it in action. For example, we have our same two equations from earlier,
3x+2y=44
6x−6y=18
So let us select just one of the equations and then isolate one of the variables.
In this case, let us chose the second equation and isolate our y value. (Why that one? Why not!)
6x−6y=18
−6y=−6x+18
y=x−3
Next, we must plug that found variable into the second equation. (In this case, because we used the second equation to isolate our y, we need to plug in that y value into the first equation.)
3x+2y=44
3x+2(x−3)=44
3x+2x−6=44
5x=50
x=10
And finally, you can find the numerical value for your first variable (y) by plugging in the numerical value you found for your second variable (x) into either the first or the second equation.
3x+2y=44
3(10)+2y=44
30+2y=44
2y=14
y=7
Or
6x−6y=18
6(10)−6y=18
60−6y=18
−6y=−42
y=7
Either way, you have found the value of both your x and y.
Again, x=10 and y=7
6x - 6y = 18 ---(2)
By using second equation,
6x - 6y = 18
x - y = 18/2 = 9
x = y +9
Substitution of value of x in terms of y in eq.1
3(y+9)+2y =44
3y + 27 + 2y = 44
5y = 44-27= 17
y = 17/5 = 3.4
So, x = y +9 = 3.4 +9 = 12.4