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4 years ago

What is the solution to the system of equations? y = 2x – 3.5 x – 2y = –14

1 answer:

katrin2010 [14]4 years ago

4 0

Hello,

Answer C

y=2x-3.5==>2x-7=3.5 (1)
x-2y=-14 (2)

(1)-2*(2)==>3y=28+3.5 ==>y=31.5/3==>y=10.5
x=-14+2*10.5==>x=7
sol={(7,10.5)}

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Use properties to rewrite the given equation. Which equations have the same solution as 3/5x +2/3 + x = 1/2– 1/5x? Check all tha

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we have

$\frac{3}{5}x+ \frac{2}{3}+x=\frac{1}{2}-\frac{1}{5}x$

Combine like terms in both sides

$(\frac{3}{5}x+ x)+\frac{2}{3}=\frac{1}{2}-\frac{1}{5}x$

we know that

$(\frac{3}{5}x+ x)=(\frac{3}{5}x+ \frac{5}{5}x)=\frac{8}{5}x$

substitute in the expression above

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Multiply equation A by $5*3*2=30$ both sides

$30*(\frac{8}{5}x+\frac{2}{3})=30*(\frac{1}{2}-\frac{1}{5}x)$

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We are going to proceed to verify each case to determine the solution.

Case a) $\frac{8}{5}x+\frac{2}{3}=\frac{1}{2}-\frac{1}{5}x$

the case a) is equal to the equation A

the case a) have the same solution that the given equation

Case b) $18x+20+30x=15-6x$

Combine like terms in left side

$(18x+30x)+20=15-6x$

$(48x)+20=15-6x$

the case b) is equal to the equation B

the case b) have the same solution that the given equation

Case c) $18x+20+x=15-6x$

Combine like terms in left side

$(18x+x)+20=15-6x$

$(19x)+20=15-6x$

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$-0.20\neq -0.09$

therefore

the case c) not have the same solution that the given equation

Case d) $24x+30x=-5$

Combine like terms in left side

$54x=-5$

the case d) is equal to the equation C

the case d) have the same solution that the given equation

Case e) $12x+30x=-5$

Combine like terms in left side

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$x=-5/42=-0.12$

$-0.12\neq -0.09$

therefore

the case e) not have the same solution that the given equation

therefore

the answer is

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case b) $18x+20+30x=15-6x$

case d) $24x+30x=-5$

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