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When you have such a system, a standard mantra to pronounce is THIS:
Left sides are identical, hence, the right sides are equal, which gives you an equation
2x + 1 = -4x + 7.
Simplify step by step and solve for x
2x + 4x = 7 - 1
6x = 6
x = 6/6 = 1.
Thus you just found "x". It is 1.
Now substitute the found value of "x" into any of the two original equations to find "y".
From the first equation, y = 2x + 1 = 2*1 + 1 = 3.
ANSWER. The solution to the system is x= 1, y= 3.
CHECK. Make checking on your own by substituting the found values x and y into original equations.
I leave it to you ---- it is necessary part of the solution (!)
Solved.
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It is a kind of the Substitution method.
When you are offered equation in this form, you are lucky: the equations are just ready for substitution.
It facilitates the remaining work.