Answer:
x=5, y=-6, or (5, -6)
Step-by-step explanation:
Hi there!
We are given the following system of equations:
6x + 3y =12
-2x-5y=20
And we want to solve it by elimination, where we will add the equations together, clear one of the variables, solve for the other variable, and then use the value of the solved variable to find the value of the first variable, that was cleared earlier
Before we clear a variable, we want the values of the coefficients to have opposite signs; for example, if we wanted to clear x in these equations, we would want the coefficients of x in both equations to be 2 and -2, or 6 and -6
In order to get the coefficients to have opposite signs, we can multiply or divide the equations by any numbers to get to the desired coefficients
For this solution, let's clear x, but you can choose to clear y if you wish; right now, the coefficients of x are 6 and -2
If we divide both sides of the first equation by 3, the equation will become 2x + y = 4, which if we add that to -2x-5y=20, we'll clear x and only have y left
In that case, take 6x + 3y =12 and divide both sides by 3
6x+3y=12
÷3 ÷3
________
2x + y = 4
Now add 2x + y =4 with -2x - 5y = 20; notice how the 2x and the -2x cancel out:
2x + y = 4
-2x-5y=20
________
0x - 4y =24
-4y=24
Divide both sides by -4
y=-6
We now have the value of y
Now we need to find the value of x
We can substitute -6 as y into either one of the equations (6x + 3y = 12 OR -2x - 5y =20) to solve for x
Let's take 6x + 3y = 12 for example
Substitute -6 as y into the equation:
6x + 3(-6) = 12
Multiply
6x - 18 = 12
Add 18 to both sides
6x = 30
Divide both sides by 6
x=5
The solution is x=5, y=-6, or as a coordinate point, (5, -6)
Hope this helps!
Want to see another example of these types of problems? Try this question! brainly.com/question/24785499
