how do you solve y=5x-8 and 5y=2x+6 using elmination?
Thank you,
Raina
multiply entire first equation by 5
5 y =25 x - 40
5 y = 2 x + 6
---------------
0 y = 23 x -46
23 x = 46
x = 2 etc
To solve the system of equations using the elimination method, you need to eliminate one variable by adding or subtracting the equations. Here's how you can solve the equations y = 5x - 8 and 5y = 2x + 6 using elimination:
Step 1: Rearrange the equations to make the coefficients of either x or y equal.
The first equation is y = 5x - 8.
The second equation is 5y = 2x + 6. To make the coefficients equal, we need to divide both sides of the equation by 5. After dividing, the second equation becomes y = (2/5)x + 6/5.
Now, the equations are y = 5x - 8 and y = (2/5)x + 6/5.
Step 2: Set the equations equal to each other.
Since both equations are now equal to y, you can set them equal to each other:
5x - 8 = (2/5)x + 6/5.
Step 3: Solve for x.
To eliminate the fraction, you can multiply the entire equation by 5:
5(5x - 8) = 5((2/5)x + 6/5).
25x - 40 = 2x + 6.
Next, isolate the x term on one side of the equation and the constant terms on the other side:
25x - 2x = 6 + 40.
23x = 46.
Divide both sides of the equation by 23:
x = 46/23.
Simplifying, we get x = 2.
Step 4: Solve for y.
Now that we know x = 2, substitute this value into one of the original equations to find y. Let's use the first equation:
y = 5(2) - 8.
y = 10 - 8.
y = 2.
Therefore, the solution to the system of equations is x = 2 and y = 2.