Final answer:
To solve the system of equations, we can use the method of substitution or elimination. After substituting the expression for x in terms of y from one equation into the other, we can solve for y. Substituting the value of y back into one of the equations will give us the value of x. The correct ordered pair is (3, 2), corresponding to option D.
Step-by-step explanation:
To solve the system of equations, we can use the method of substitution or elimination. Let's use the method of substitution:
Step 1: Solve one equation for one variable in terms of the other variable.
From the second equation, we can solve for x:
4x - 3y = 6
4x = 3y + 6
x = (3y + 6) / 4
Step 2: Substitute the expression from step 1 into the other equation.
Substituting (3y + 6) / 4 for x in the first equation:
5((3y + 6) / 4) + 2y = 19
15y + 30 + 8y = 76
23y = 46
y = 2
Step 3: Substitute the value of y back into one of the original equations to solve for x.
Using the second equation:
4x - 3(2) = 6
4x - 6 = 6
4x = 12
x = 3