Question

What is the solution to this system of equations? 4x + 5y = 7 3x – 2y = –12

Answer 1

The answer is (-2,3)

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Answer 2

Answer:   (x, y) = (-2, 3) is the required solution.

Step-by-step explanation:  We are given to find the solution to the following system of linear equations:

$4x+5y=7~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\3x-2y=-12~~~~~~~~~~~~~~~~~~~(ii)$

Multiplying equation (i) by 3 and equation (ii) by 4, we have

$12x+15y=21~~~~~~~~~~~~~~~~~(iii)\\\\12x-8y=-48~~~~~~~~~~~~~~~~(iv)$

Subtracting equation (iv) from equation (iii), we get

$(12x+15y)-(12x-8y)=21-(-48)\\\\\Rightarrow 12x+15y-12x+8y=21+48\\\\\Rightarrow 23y=69\\\\\Rightarrow y=3,$

and from equation (i), we get

$4x+5\times 3=7\\\\\Rightarrow 4x+15=7\\\\\Rightarrow 4x=-8\\\\\Rightarrow x=-2.$

Therefore, the solution to the given system is  x = - 2, y = 3.

Thus, (x, y) = (-2, 3) is the required solution.