Question

Solve Systems of Equations Using the Substitution Method

6x - y= -4
2x + 2y = 15

I genuinely do not understand this concept at all, it would be AMAZING, if you could explain this as well.
Thanks, all.

Answer 1

x= ½, y= 7

Explanation:

`\textcolor{steelblue}{\text{\textcircled{1} Label the equations}}`

6x -y= -4 -----(1)

2x +2y= 15 -----(2)

`\textcolor{steelblue}{\text{\textcircled{2} Make y the subject of formula}}`

We could also make x the subject of formula in one equation, however the equation can be easily rearranged so that the coefficient of y is 1. This can be done by moving the y term to the right hand side of the equation, and the rest to the left. Note that each time you bring a term or constant over to the other side of the equation, its sign changes (e.g. positive to negative).

From (1):

6x +4= y

y= 6x +4 -----(3)

Label the equation as equation (3) so we can refer to it easily later.

`\textcolor{steelblue}{\text{\textcircled{3} Substitute (3) into (2)}}`

Now that we have an equation of y that is written in terms of x, we can replace all the y in equation (2) so that the whole equation is only in terms of x.

Subst. (3) into (2):

2x +2(6x +4)= 15

Expand:

2x +12x +8= 15

Simplify:

14x +8= 15

14x= 15 -8

14x= 7

x= 7 ÷14

x= ½

`\textcolor{steelblue}{\text{\textcircled{4} Find y}}`

Substitute x= ½ into (3):

y= 6(½) +4

y= 3 +4

y= 7