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Question 466775: using the elimination method solve 3x+4y=5 and 2x+y=1. Please show all your work.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the elimination method applies multiplication factors to each equation, as required, so that when you add the equations to each other, or subtract the equations from each other, one of the variables will disappear and you will be left with one equation in one unknown which you can then solve. once you have solved for one of the variables, you can then use that value to help solve for the other variable.
your equations are:
3x + 4y = 5
2x + y = 1
if you multiply the second equation by 4, you will be able to eliminate the y from the equation and you can then solve for x.
when you multiply an equation, you have to multiply both sides of the equation in order to preserve the equality.
multiplying the second equation by 4 gets you:
3x + 4y = 5 (first equation)
8x + 4y = 4 (second equation multiplied by 4)
if you subtract the first equation from the second equation, you will be left with:
5x = -1
divide both sides of this equation by 5 and you get:
x = -1/5
you can now substitute for x in either of the 2 original equations in order to solve for y.
using the first equation of:
3x + 4y = 5
substitute (-1/5) for x to get:
3*(-1/5) + 4y = 5
simplify to get:
(-3/5) + 4y = 5
add (-3/5) to both sides of the equation to get:
4y = 5 + (3/5) which becomes:
4y = 28/5
divide both sides of this equation by 4 to get:
y = 7/5
the 2 values for x and y are:
x = -1/5
y = 7/5
substitute for x and y in the first original equation of:
3x + 4y = 5 to get:
3*(-1/5) + 4*(7/5) = 5 which becomes:
-3/5 + 28/5 = 5 which becomes:
25/5 = 5 which becomes:
5 = 5, confirming the values for x and y are solutions for the first equation.
substitute for x and y in the second original equation of:
2x + y = 1 to get:
2*(-1/5) + (7/5) = 1 which becomes:
-2/5 + 7/5 = 1 which becomes:
5/5 = 1 which becomes:
1 = 1, confirming the values for x and y are solutions for the second equation.
those are your answers:
x = -1/5
y = 7/5
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