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use all three methods graphing,substitution,linear combination to solve 7x-3y=4 and -14x+6y=-8

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1 Answer

Hi Angelica;
7x-3y=4 and -14x+6y=-8
 
LINEAR COMBINATION
This equations are linear combinations.  Both equations have variables x and y with coefficients A and B.
Furthermore, the first equation is in standard format...
Ax+By=C, neither A nor B equal zero and A is greater than zero.
7x-3y=4
However, the second equation is NOT in standard format in that A is less than zero...
-14x+6y=-8
Let's fix that by multiplying both sides by -1...
-1(-14x+6y)=(-8)(-1)
14x-6y=8
 
SUBSTITUTION
7x-3y=4 and 14x-6y=8
Let's take the first equation...
7x-3y=4
Let's multiply both sides by 2...
(2)(7x-3y)=(4)(2)
14x-6y=8
It is identical to the second equation.
 
ZERO SOLUTIONS ARE POSSIBLE BECAUSE BOTH EQUATIONS ARE IDENTICAL.

Comments

Hi Angelica;
Both equations are the same line.  There is no solution.  You can graph the line.  The slope is -A/B of the standard equation, -(7/-3)=7/3.  As the line rises 7 units, it moves to the right 3 units.  You can also establish the y-intercept, value of y when x=0, as well as the x-intercept, value of x when y=0.
7x-3y=4
x-intercept, (4/7,0)
y-intercept, (0,-4/3)
And that is all you can do.