Solve the following system of equations. You will type your x value in the first part and the y value in the second part of the question. If the answer is no solution then type NS in both parts and if the the answer is infinite solutions then type I in both parts.
y = 2/5 x- 17 7/10
y = -5/2 x + 20
What is the x value?
subtract eq2 from 1
0=(2/5+2.5)x -17.7-20
0=(2.9x)-37.7
x=37.7/2.9
for y, put that value of x into either equation, and solve for y.
Since the two y values must be the same ....
2/5 x- 17 7/10 = -5/2 x + 20
2x/5 - 177/10 = -5x/2 + 20
I suggest we multiply each term by 10
4x - 177 = -25x + 200
take over , (the x value is a whole number, but the y isn't)
To solve this system of equations, we can use the method of substitution or elimination. Let's use the method of substitution in this case.
Step 1: Start by rearranging one of the equations to solve for one variable in terms of the other. Let's rearrange the second equation to solve for y:
y = -5/2x + 20
Step 2: Substitute the value of y from the second equation into the first equation. So, we substitute -5/2x + 20 for y in the first equation:
-5/2x + 20 = 2/5x - 17 7/10
Step 3: Simplify and solve for x:
Multiply both sides of the equation by 10 to clear the fractions:
-5x + 200 = 4x - 177
Add 5x to both sides of the equation:
200 = 9x - 177
Add 177 to both sides of the equation:
377 = 9x
Divide both sides of the equation by 9:
x = 377/9
Step 4: Simplify the fraction:
x ≈ 41.89
So, the approximate value of x is 41.89.
Now, you can find the y value by substituting this x value back into either of the original equations. Let's substitute x = 41.89 into the second equation:
y = -5/2(41.89) + 20
y = -104.73 + 20
y ≈ -84.73
So, the approximate value of y is -84.73.
Therefore, the solution to the system of equations is x ≈ 41.89 and y ≈ -84.73.