Find the x- and y- of each equation.
x + y = 9
and
x - 2y = 2
subtract the equations
3y=7
solve for y.
then,x=9-y
Where did you get 3y=7 from?
To find the values of x and y for each equation, we can use the method of substitution or the method of elimination.
Method 1: Substitution
1. Solve one equation for one variable in terms of the other variable. Let's solve the first equation for x:
x = 9 - y
2. Substitute the value of x in the second equation:
(9 - y) - 2y = 2
3. Simplify and solve for y:
9 - 3y = 2
-3y = 2 - 9
-3y = -7
y = -7 / -3
y = 7/3
4. Substitute the value of y back into the first equation to find x:
x + (7/3) = 9
x = 9 - (7/3)
x = 27/3 - 7/3
x = 20/3
Therefore, the solutions to the equations are x = 20/3 and y = 7/3.
Method 2: Elimination
1. Multiply the first equation by 2 and the second equation by 1 to make the coefficients of y the same:
2(x + y) = 2(9) -> 2x + 2y = 18
1(x - 2y) = 1(2) -> x - 2y = 2
2. Subtract the second equation from the first equation to eliminate y:
(2x + 2y) - (x - 2y) = 18 - 2
2x + 2y - x + 2y = 16
x + 4y = 16
3. Solve the resulting equation for one variable in terms of the other:
x = 16 - 4y
4. Substitute the value of x into either of the original equations:
(16 - 4y) + y = 9
5. Simplify and solve for y:
16 - 4y + y = 9
-3y = 9 - 16
-3y = -7
y = -7 / -3
y = 7/3
6. Substitute the value of y back into the first equation to find x:
x + (7/3) = 9
x = 9 - (7/3)
x = 27/3 - 7/3
x = 20/3
Therefore, the solutions to the equations are x = 20/3 and y = 7/3.