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21x+7y=42
−5x+5y=10
what would x and y be? I am not sure how to solve these problems if the equations don't equal y.
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Your starting equations are
21x + 7y = 42 (1)
−5x + 5y = 10 (2)
In the first equation, divide both sides by 7.
In the second equation, divide both sides by 5. You will get an EQUIVALENT system of equations
3x + y = 6 (3)
-x + y = 2. (4)
From equation (3), subtract equation (4). You will get then, after canceling the terms with "y"
3x - (-x) = 6 - 2
4x = 4
x = 4/4 = 1.
Next, substitute x= 1 into equation (4). You will get
-1 + y = 2,
or y = 2 + 1 = 3.
ANSWER. The solution to the given system opf equations is x= 1, y= 3.
CHECK. Check it ON YOUR OWN, that the found values x= 1, y= 3 satisfy the given equations (1) and (2).
Solved and explained.
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As I see from your post, the level of your knowledge is about zero on this subject.
On solving systems of linear equations, see the lessons
- Solution of the linear system of two equations in two unknowns by the Substitution method
- Solution of the linear system of two equations in two unknowns by the Elimination method
in this site.