To solve for y and x in the equation x+2y=7, you can use either substitution or elimination method.
1) Substitution method:
Rearrange the equation to solve for x in terms of y:
x = 7 - 2y
Now substitute this expression for x in the equation:
(7 - 2y) + 2y = 7
Simplify:
7 - 2y + 2y = 7
Combine like terms:
7 = 7
This equation is true for any value of y, meaning y can take on any value.
To solve for x, substitute y = 0 into the equation:
x = 7 - 2(0) = 7
So the solution is (x, y) = (7, y) where y can be any real number.
2) Elimination method:
Multiply both sides of the equation by -2 to eliminate the y term:
-2(x + 2y) = -2(7)
-2x - 4y = -14
Rearrange the equation to solve for x in terms of y:
-2x = -4y - 14
Divide both sides by -2:
x = 2y + 7
Now the equation is in the form x = 2y + 7.
This equation represents a line in the coordinate plane where the slope is 2 and the y-intercept is 7.
The solution is (x, y) = (2y + 7, y) where y can be any real number.
Solve for y and x
x+2y=7
1 answer