Which is the best approximation for the solution of the system of equations? y=-2/5x+1 y=3x-2

x = 15/17  , y = 11/17

Step-by-step explanation:

Solve the following system:

{y = 1 - (2 x)/5 | (equation 1)

{y = 3 x - 2 | (equation 2)

Express the system in standard form:

{(2 x)/5 + y = 1 | (equation 1)

{-(3 x) + y = -2 | (equation 2)

Swap equation 1 with equation 2:

{-(3 x) + y = -2 | (equation 1)

{(2 x)/5 + y = 1 | (equation 2)

Add 2/15 × (equation 1) to equation 2:

{-(3 x) + y = -2 | (equation 1)

{0 x+(17 y)/15 = 11/15 | (equation 2)

Multiply equation 2 by 15:

{-(3 x) + y = -2 | (equation 1)

{0 x+17 y = 11 | (equation 2)

Divide equation 2 by 17:

{-(3 x) + y = -2 | (equation 1)

{0 x+y = 11/17 | (equation 2)

Subtract equation 2 from equation 1:

{-(3 x)+0 y = -45/17 | (equation 1)

{0 x+y = 11/17 | (equation 2)

Divide equation 1 by -3:

{x+0 y = 15/17 | (equation 1)

v0 x+y = 11/17 | (equation 2)

Collect results:

{x = 15/17  , y = 11/17

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.