Question

4x-7y=15 and 5x-2y=12

Answer 1

Presumably we're being asked to solve the system.  

4x - 7y = 15

5x - 2y = 12

We don't really have any common factors among the coefficients of x, or among the coefficients of y, so we can do the general thing. To eliminate y multiply the first equation by (typically the absolute value of) the coefficient of y in the second equation and vice verse, then add or subtract equations to eliminate.  

First equation times 2:

8x - 14y = 30

Second equation times 7:

35x - 14y = 84

Subtract,

27x = 54

x = 54/27 = 2

2y = 5x - 12 = 10 - 12 = -2

y = -1

Answer: x=2, y = -1

Check:

4(2)-7(-1)=8+7=15, good

5(2) -2(-1) = 10 + 2 = 12, good

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If you do enough of these 2x2 linear systems you can learn to just write down the answer.  I usually remember the matrix inverse, but if you haven't gotten there you can just remember the pattern:  

ax + by = c    

dx + ey = f

has solutions

x = (ce-bf)/(ae-bd), y = (a f-cd)/(ae-bd)

4x - 7y = 15    

5x - 2y = 12

has solutions

denom = ae-bd = 4(-2) - (-7)(5) = 27

x = (15(-2) - (-7)(12))/27 = (-30 + 84)/27 = 2

y = (4(12)-15(5))/27 = (48-75)/27 = -27/27 = -1

Answer 2

Answer:

Step-by-step explanation:

4x-7y=15                          

Add '-7y' to each side of the equation.    

Add '2y' to each side of the equation.

5x + -2y + 2y = 12 + 2y

Combine like terms: -2y + 2y = 0

5x + 0 = 12 + 2y

5x = 12 + 2y

Divide each side by '5'.

x = 2.4 + 0.4y

Simplifying

x = 2.4 + 0.4y

4x + 7y + -7y = 15 + -7y

Combine like terms: 7y + -7y = 0

4x + 0 = 15 + -7y

4x = 15 + -7y