A system of equations is shown:

4x = −3y + 17
3x − 4y = −6

What is the solution to this system of equations?
(−2, −3)
(3, 2)
(2, 3)
(−3, −2)

Using substitution, it is found that the solution of the system of equations is: (2,3).

The equations are:

From the second equation:

Replacing in the first:

Multiplying everything by 3:

Then:

Then, the solution is (2,3).

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(2, 3)

Step-by-step explanation:

Given:  4x = −3y + 17  and  3x − 4y = −6

4x = -3y + 17

∴ 4x + 3y = 17  ⇒ (1)

   3x − 4y = −6 ⇒ (2)

Multiplying eq.(1) by 4 and eq.(2) by 3

16x + 12y = 68

9x - 12y = -18

Add the last 2 equations, the y terms will be eliminated

16x + 9x = 68 - 18

25x = 50

∴ x = 50/25 = 2

By substitution with x at eq.(1)

4*2 + 3y = 17

8 + 3y = 17

3y = 17 - 8 = 9

∴ y = 9/3 = 3

So, x = 2 and y = 3

The solution to this system of equations is (2,3)

Also see the attached figure which represent the graphical solution for the given system of equations

step-by-step explanation: