Question 708800
Let A = th eage of the dad
Let B = the age of the son
Equation 1: {{{A = 4B}}}
Equation 2: {{{A - 6 = 10*(B-6)}}}
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Since equation 1 is solved for A, plug 4B into equation 2 for A
Equation 2: {{{A - 6 = 10*(B-6)}}}
{{{(4B) - 6 = 10*(B-6)}}}
Multiply the 10 through
{{{4B - 6 = 10B - 60}}}
Subtract 4B from both sides
{{{-6 = 6B - 60}}}
Add 60 to both sides
{{{54 = 6B}}}
Divide both sides by 6
{{{highlight(9 = B)}}}
Now plug 9 into equation 1 for B
Equation 1: {{{A = 4B}}}
{{{A = 4*(9)}}}
{{{highlight_green(A = 36)}}}

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Extra question #1:
The line y=mx+c passes through (2'5) and (4'13). Find the m and the c.
In that equation m is the slope and c is the Y-intercept.
Points on a graph are given in the form (X,Y).
The equation to find the slope of the line between to points is:
{{{m = (Y2-Y1)/(X2-X1)}}}
Now we will plug in the values you were given to solve for m.
{{{m = (13-5)/(4-2)}}}
{{{m = 8/2}}}
{{{highlight_green(m = 4)}}}
Since we know what m equals, we can rewrite the equation of the line.
y = mx+c is now y = 4x+c
The next step is to pick one of the points that you were gven and solve for c.
I will you the point (2,5)
That means that when x=2, then y=5
Plug those values into the line equation
{{{y = 4x + c}}}
{{{5 = 4*2 + c}}}
{{{5 = 8 + c}}}
Subtract 8 from both sides
{{{highlight(-3 = c)}}}
The equation of the line that passes through the given points is y = 4x - 3

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Extra question #2:
Twice one Number added to 3 times a nother gives 21. Find the numbers if the difference between them is 3.
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Equation 1: {{{2A + 3B = 21}}}
Equation 2: {{{A = B + 3}}}
Since equation 2 is solved for A, plug (B + 3) into equation 1 for A.
Equation 1: {{{2A + 3B = 21}}}
{{{2*(B + 3) + 3B = 21}}}
Multiply the 2 through
{{{2B + 6 + 3B = 21}}}
Combine like terms
{{{5B + 6 = 21}}}
Subtract 6 from both sides
{{{5B = 15}}}
Divide both sides by 5
{{{highlight(B = 3)}}}
Now plug 3 into equation 2 for B.
Equation 2: {{{A = B + 3}}}
{{{A = (3) + 3}}}
{{{highlight_green(A = 6)}}}