To solve this system of equations using elimination, we need to eliminate one variable by adding or subtracting the equations. In this case, we will eliminate the x variable.
To eliminate the x variable, we can multiply the first equation by 7 and the second equation by 3 so that the coefficients of x in both equations will be equal.
Multiplying the first equation by 7 gives us:
7(3x + 3y) = 7(0)
21x + 21y = 0
Multiplying the second equation by 3 gives us:
3(-7x - 9y) = 3(18)
-21x - 27y = 54
Now we have a system of equations with equal x coefficients, so we can subtract the two equations to eliminate x.
(21x + 21y) - (-21x - 27y) = 0 - 54
21x + 21y + 21x + 27y = -54
42x + 48y = -54
Dividing the equation by 6 to simplify and solve for y:
(42/6)x + (48/6)y = (-54/6)
7x + 8y = -9
We now have a new equation, 7x + 8y = -9, and the equation 3x + 3y = 0 from the original system.
To eliminate the y variable, we can multiply the second equation by 8 and the first equation by 3:
Multiplying the second equation by 8 gives us:
8(3x + 3y) = 8(0)
24x + 24y = 0
Multiplying the first equation by 3 gives us:
3(7x + 8y) = 3(-9)
21x + 24y = -27
Now we have a system of equations with equal y coefficients, so we can subtract the two equations to eliminate y.
(24x + 24y) - (21x + 24y) = 0 - (-27)
24x + 24y - 21x - 24y = 27
3x = 27
Simplifying by dividing both sides of the equation by 3 gives us:
x = 9
Now that we have the value of x, we can substitute it back into one of the original equations to solve for y. We'll use the first equation:
3x + 3y = 0
3(9) + 3y = 0
27 + 3y = 0
3y = -27
y = -9
Therefore, the solution to the system of equations is x = 9 and y = -9.
Solve the system of equations using elimination: 3, x, plus, 3, y, equals, 03x+3y=0 and minus, 7, x, minus, 9, y, equals, 18−7x−9y=18.
1 answer
1 answer