Answer
The solution of the system will be ordered pair $(6,\frac{1}{2})$.
Work Step by Step
Equation 1: $x + 2y = 7$
Equation 2: $2x + 2y = 13$
Multiply equation 2 by $-1$:
$$[2x + 2y = 13]\cdot-1$$ $$-2x - 2y = -13$$
Add this equation to equation 1:
$$-2x - 2y = -13$$ $$+$$ $$x + 2y = 7$$ $$=$$ $$-x=-6$$ $$x=6$$
Substitute this value to equation 1:
$$x + 2y = 7$$ $$6 + 2y = 7$$
Subtract $6$ from both sides:
$$6 -6+ 2y = 7-6$$ $$2y=1$$
Divide both sides by $2$:
$$\frac{2y}{2}=\frac{1}{2}$$ $$y=\frac{1}{2}$$
Check using equation 2:
$$2x + 2y = 13$$ $$2(6) + 2(\frac{1}{2}) = 13$$ $$12+1=13$$ $$13=13$$
Therefore, the solution of the system will be ordered pair $(6,\frac{1}{2})$.
