The ordered pair of the given system of equation is (3,5). So option C is the correct answer.
The given equations are 4x+7y=47 and 5x-4y=-5.
Solve for the first variable in one of the equations, then substitute the result into the other equation.
What is the elimination method in the system of equations?
In the elimination method, you either add or subtract the equations to get an equation in one variable. When the coefficients of one variable are opposites you add the equations to eliminate a variable and when the coefficients of one variable are equal you subtract the equations to eliminate a variable.
Now, 4x+7y=47------(1) and 5x-4y=-5-----(2)
Multiply equation (1) by 4 and equation (2) by 7.
That is 16x+28y=188------(3) and 35x-28y=-35
Add equation(3) and (4)
16x+28y+35x-28y=188-35
⇒51x=153
⇒x=3
Substitute x=3 in equation (1).
That is 4×3+7y=47
⇒7y=35
⇒y=5
Therefore, the ordered pair of the given system of equation is (3,5). So option C is the correct answer.
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