How do you solve system of equation problem. example
x+3y=32
-3x+2y+3
and
x+y=6
x-y=-9
x + 3y = 32
-3x + 2y = 3
Add 3x1st to 2nd to produce
11y = 99
y = 9
so,
x = 5
___________
x + y = 6
x - y = -9
add the two equations to get
2x = -3
x = -3/2
so,
y = 15/2
To solve a system of equations, you can use a method called "substitution" or "elimination" to find the values of the variables that make both equations true. Let's solve the given examples:
Example 1:
Equation 1: x + 3y = 32
Equation 2: -3x + 2y = -3
Method: Substitution
1. Solve Equation 1 for x:
x = 32 - 3y
2. Substitute the value of x in Equation 2:
-3(32 - 3y) + 2y = -3
-96 + 9y + 2y = -3
11y = 93
y = 93/11
y = 8.45 (rounded to two decimal places)
3. Substitute the value of y back into Equation 1 to find x:
x + 3(8.45) = 32
x + 25.35 = 32
x = 32 - 25.35
x = 6.65 (rounded to two decimal places)
Therefore, the solution for the system of equations is x = 6.65 and y = 8.45.
Example 2:
Equation 1: x + y = 6
Equation 2: x - y = -9
Method: Elimination
1. Add both equations to eliminate the variable y:
(x + y) + (x - y) = 6 + (-9)
2x = -3
x = -3/2
x = -1.5
2. Substitute the value of x back into either of the original equations to find y:
-1.5 + y = 6
y = 6 + 1.5
y = 7.5
Therefore, the solution for the system of equations is x = -1.5 and y = 7.5.
Remember to double-check your solution by substituting the values of x and y into both equations.