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mariarad [96]
4 years ago
15

Which statement is true about the equations –3x + 4y = 12 and x – y = 1? The system of the equations has exactly one solution at

(–8, 3). The system of the equations has exactly one solution at (–4, 3). The system of the equations has no solution; the two lines are parallel. The system of the equations has an infinite number of solutions represented by either equation.
Mathematics
1 answer:
ElenaW [278]4 years ago
3 0
The equations are:
                        -3x + 4y = 12
                           x - y = 1

We solve for the solution by the substitution method. From the second equation,
                          x = 1 + y

We substitute x of the first equation with the expression derived above.
 
                       -3(1 + y) + 4y = 12
                           -3 -3y + 4y = 12
                               y - 3 = 12
Transposing,
                                   y = 15
Substituting this to the expression for x,
                       x = 1 + y = 1 + 15 = 16

Thus, the solution is (16,15). 

Thus, the equations has exactly one solution which is equal to (16,15). 
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Answer:

3x+2y=315\\\\2x+4y=450

is the system of equations representing the situation.

Step-by-step explanation:

Given:

Alexandra finds that she can give 3 haircuts and 2 hair dyes in 315 minutes. Giving 2  haircuts and 4 hair dyes takes 450 minutes.

Now, to find the system of equations representing the situation.

<u><em>Let the number of haircuts be </em></u>x.<u><em /></u>

<u><em>Let the number of hair dyes be </em></u>y.<u><em /></u>

So, Alexandra can give 3 haircuts and 2 hair dyes in:

3x+2y=315.

Now, giving 2 haircuts and 4 hair dyes in:

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Therefore,

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