To solve the system using elimination, we need to eliminate one of the variables by multiplying one or both equations by appropriate constants. In this case, we can eliminate the x variable by multiplying the second equation by 5 and the first equation by 3. This will make the coefficients of x in both equations the same and allow us to eliminate x by subtracting the two equations.
First, let's multiply the second equation by 5:
5(3x - 3y) = 5(18)
15x - 15y = 90
Next, let's multiply the first equation by 3:
3(5x + 4y) = 3(12)
15x + 12y = 36
Now we have the system of equations:
15x + 12y = 36
15x - 15y = 90
To eliminate x, we can subtract the second equation from the first equation:
(15x + 12y) - (15x - 15y) = 36 - 90
This simplifies to:
15x + 12y - 15x + 15y = -54
Combining like terms:
27y = -54
To solve for y, divide both sides of the equation by 27:
27y/27 = -54/27
y = -2
Now that we have the value of y, we can substitute it back into either of the original equations to solve for x. Let's use the first equation:
5x + 4(-2) = 12
Simplifying:
5x - 8 = 12
To solve for x, add 8 to both sides:
5x = 12 + 8
5x = 20
Divide both sides of the equation by 5:
x = 20/5
x = 4
So the solution to the system of equations is x = 4 and y = -2.
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Solve the system using elimination.
5x + 4y = 12
3x – 3y = 18
(3 points)
1 answer
2 answers