I am trying to solve the sytems of equations using the elimination method.
2x+4y=10
-3x+3y=-6
I tied multiplying the first equation by 2 and the second by 4. Then I tried multiplying the first equation by -3 and the secondy by 3.
The book says the answers are 3,1.
I am not getting these answers.
Try to multiply first equation by 3 and second equation by 2. You will end up with 6x and -6x, you can eliminate those and then use the substitution method to find y.
Multiply the second equation by 2/3
2x+4y=10
-2x+2y=-4
add the equations
6y=6
y=1
Put that y back into either equation, and solve for x.
To solve the system of equations using the elimination method, you need to eliminate one variable by adding or subtracting the two equations. Let's go step by step to solve the given system of equations:
Given equations:
1) 2x + 4y = 10
2) -3x + 3y = -6
Step 1: Choose a variable to eliminate.
In this case, you can choose either x or y to eliminate. Since the coefficients of y in both equations are already the same, we can eliminate y by multiplying the first equation by -3 and the second equation by 4.
Step 2: Multiply the equations.
Multiply equation 1 by -3: -6x - 12y = -30
Multiply equation 2 by 4: -12x + 12y = -24
Now, you have:
-6x - 12y = -30
-12x + 12y = -24
Step 3: Add the equations.
Combine the two equations by adding them:
(-6x - 12y) + (-12x + 12y) = -30 + (-24)
-6x - 12y - 12x + 12y = -30 - 24
-18x = -54
Step 4: Solve for x.
Divide both sides of the equation by -18:
x = (-54) / (-18)
x = 3
Step 5: Substitute the value of x into one of the original equations to solve for y.
Let's substitute x = 3 into equation 1:
2x + 4y = 10
2(3) + 4y = 10
6 + 4y = 10
4y = 10 - 6
4y = 4
y = 4 / 4
y = 1
Therefore, the solution to the system of equations is x = 3 and y = 1.