solve the systems of equations by elimination.
6x-y=18
2x+y=7
See your first post.
Follow that example to complete this problem. Same concept, different numbers.
To solve the system of equations by elimination, you need to eliminate one variable by adding or subtracting the two equations. Here's how you can do it:
1. Rearrange the two equations in a way that aligns the variables:
6x - y = 18
2x + y = 7
2. Notice that the coefficient of the y term in the first equation is -1, and in the second equation is +1. To eliminate the y term, add the two equations together:
(6x - y) + (2x + y) = 18 + 7
Simplify the equation:
6x + 2x - y + y = 25
Combine like terms:
8x = 25
3. Now, solve for x by dividing both sides of the equation by 8:
8x/8 = 25/8
x = 25/8
Therefore, x = 3.125.
4. To find the value of y, substitute the value of x back into either of the original equations. Let's use the first equation:
6x - y = 18
Substitute x = 3.125:
6(3.125) - y = 18
Simplify:
18.75 - y = 18
Now, isolate y by subtracting 18.75 from both sides:
-y = 18 - 18.75
Simplify:
-y = -0.75
Divide both sides of the equation by -1 to solve for y:
y = 0.75
So, the solution to the system of equations is x = 3.125 and y = 0.75.