Question 656022: use the method of substitution to solve the system of linear equations
3x-y=5
7x-2y=12
the solution is _______(order pair) Found 2 solutions by MathDazed, MathTherapy:Answer by MathDazed(34) (Show Source):
You can put this solution on YOUR website! 3x - y = 5........(i)
7x - 2y = 12......(ii)
To use the substitution method, you will have to solve for one of the variables. I chose to use equation (i) and solve for y.
3x - y + y = 5 + y
3x = 5 + y
3x - 5 = 5 - 5 + y
3x - 5 = y.........(iii)
Substitute equation (iii) into equation (ii)
7x - 2(3x-5) = 12
7x - 6x + 10 = 12
x + 10 - 10 = 12 - 10
x = 2
Substitute x = 2 into (iii)
3(2) - 5 = y
6 - 5 = y
y = 1
Solution (2,1)
For the substitution method, one of the equations has to be solve for one of the two variables. Since y in eq (i) has a coefficient of - 1, we'll solve for y in that equation.
3x - y = 5
3x - 5 = y
Substitute 3x - 5 for y in eq (ii). This will allow you to determine the value of x. Knowing the value of x you can then determine the value of y. You can then substitute the values of x and y into each equation to see if the values make the equations true. If they do, then that's it!!
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