Solve each system using elimination.
1.) 5x - y=0
3x + y=24
2.) 3x + 3y =27
x - 3y =-11
3.) 6x +4y =42
-3x + 3y =-6
5x - y = 0
3x + y = 24
8x = 24
x = 3
5(3) - y = 0
15 - y = 0
15-15 - y = 0 -15
-y = -15
y = 15
( 3, 15)
2)
3x +3y = 27
x - 3y = -11
4x = 16
x = 4
4 - 3y = -11
4-4 - 3y = -11 -4
-3y = -15
y = 5
(4, 5)
3)
6x + 4y = 42
2(-3x + 6y = -6)
6x + 4y = 42
-6x + 6y = -12
10y = 30
y = 3
-3x + 3(3) = -6
-3x +9 = -6
-3x + 9 -9 = -6 - 9
- 3x = -15
x = 5
(5, 3)
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To solve each system using elimination, we need to eliminate one variable by adding or subtracting the equations.
1.) 5x - y = 0
3x + y = 24
To eliminate the y variable, we can add the two equations together.
(5x - y) + (3x + y) = 0 + 24
8x = 24
Now, we can solve for x by dividing both sides of the equation by 8.
8x/8 = 24/8
x = 3
To find the value of y, substitute the value of x back into one of the original equations. Let's use the first equation.
5x - y = 0
5(3) - y = 0
15 - y = 0
Now, solve for y.
-y = -15
y = 15
Therefore, the solution to the system is x = 3 and y = 15.
2.) 3x + 3y = 27
x - 3y = -11
To eliminate the y variable, we can multiply the second equation by 3.
3(x - 3y) = 3(-11)
3x - 9y = -33
Now, we can add the two equations together to eliminate the y variable.
(3x + 3y) + (3x - 9y) = 27 + (-33)
6x = -6
To solve for x, divide both sides of the equation by 6.
6x/6 = -6/6
x = -1
To find the value of y, substitute the value of x back into one of the original equations. Let's use the second equation.
x - 3y = -11
(-1) - 3y = -11
-1 - 3y = -11
Now, solve for y.
-3y = -10
y = 10/3 or 3.33 (rounded to two decimal places)
Therefore, the solution to the system is x = -1 and y = 3.33 or approximately 3.33.
3.) 6x + 4y = 42
-3x + 3y = -6
To eliminate the x variable, we can multiply the second equation by 2.
2(-3x + 3y) = 2(-6)
-6x + 6y = -12
Now, we can add the two equations together to eliminate the x variable.
(6x + 4y) + (-6x + 6y) = 42 + (-12)
10y = 30
To solve for y, divide both sides of the equation by 10.
10y/10 = 30/10
y = 3
To find the value of x, substitute the value of y back into one of the original equations. Let's use the second equation.
-3x + 3y = -6
-3x + 3(3) = -6
-3x + 9 = -6
Now, solve for x.
-3x = -15
x = 5
Therefore, the solution to the system is x = 5 and y = 3.