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3 years ago

Find a solution to the following system of equations. -2x + y = -3 -x + 2y = 3

Mathematics

2 answers:

GalinKa [24]3 years ago

5 0

Answer:

Step-by-step explanation: 3+2=5

Serhud [2]3 years ago

3 0

Answer: x=3 y=3

Elimination method.

eliminating x and solving for y.

-2x +y=-3

-x+2y=3

-2(-x+2y=3)

2x -4y = 6

Multiply the second equation by -2 so the x’s cancel out.

-2x+y=-3

2x-4y=6

-2x and 2x cancels out

Add like terms

y-=-6

4y=-3

solve.

-3y = -9

divide by -3 on both sides and

y=3

Plug in 3 for the place of y in either either equation.

-2x+ 3= -3

solve for x.

-2x+ 3= -3

-3 -3

-2x=-6

Divide by -2

x=3

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3 years ago

total number of boys and girls in a class is 42. if the number of girls is 10 more than the boys find the number of boys?? answe

dsp73

Answer:

$\boxed{\sf Total \ number \ of \ boys = 16}$

Given:

Total number of boys and girls in class = 42

Total number of girls = 10 more than the boys

To Find:

Total number of boys

Step-by-step explanation:

Let total number of boys be 'x'

$\sf So, \\ \sf Total \: number \ of \ girls = x + 10 \\ \\ \therefore \\ \sf \implies Total \: number \: of \: boys \: and \: girls \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: = Total \: number \: of \: boys + Total \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: number \: of \: girls \\ \\ \sf \implies 42 = x + (x + 10) \\ \\ \sf 42 = x + (x + 10) \: is \: equivalent \: to \: x + (x + 10) = 42 : \\ \sf \implies x + (x + 10 )= 42 \\ \sf \implies x + x + 10 = 42 \\ \\ \sf x + x = 2x : \\ \sf \implies \boxed{ \sf 2x} + 10 = 42$

$\sf Substrate \: 10 \: from \: both \: sides : \\ \sf \implies 2x + (10 - \boxed{ \sf 10}) = 42 - \boxed{ \sf 10} \\ \\ \sf 10 - 10 = 0 : \\ \sf \implies 2x = 42 - 10 \\ \\ \sf 42 - 10 = 32 : \\ \sf \implies 2x = \boxed{ \sf 32} \\ \\ \sf Divide \: both \ sides \: by \: 2 : \\ \sf \implies \frac{2x}{ \boxed{ \sf 2}} = \frac{32}{ \boxed{ \sf 2}} \\ \\ \sf \frac{2x}{2} = \frac{ \cancel{2}}{ \cancel{2}} \times (x) = x : \\ \sf \implies x = \frac{32}{2} \\ \\ \sf \frac{32}{2} = \frac{16 \times \cancel{2}}{ \cancel{2}} = 16 : \\ \sf \implies x = 16$