Final answer:
The solution to the system of equations y=(-7/2)x and 2y=-2x-1 is x = 1/5 and y = -7/10 after solving for x and then substituting it into one of the equations to find y.
Step-by-step explanation:
Solving systems of equatios involves finding the set of values that satisfy all equations simultaneously. In this question, we need to solve the system y=(-7/2)x and 2y=-2x-1 simultaneously. First, we identify that the equations are already in slope-intercept form, which is y=mx+b, where m is the slope and b is the y-intercept.
Let's rewrite the second equation to make it clearer: 2y=-2x-1 becomes y=-x-1/2 when divided by 2. Now we have two simplified equations:
- y=(-7/2)x
- y=-x-1/2
Since both equations equal y, we can set them equal to each other to find the value of x:
(-7/2)x = -x - 1/2. By solving for x, we get the value that satisfies both equations. Then we can substitute x back into any of the original equations to find the corresponding y value.
To solve the equation, first get rid of the fractions by multiplying through by 2, so we have:
-7x = -2x - 1
Moving like terms to the same side gives us:
-7x + 2x = -1
Which simplifies to:
-5x = -1
And finally, dividing by -5 gives us:
x = 1/5
Substitute x = 1/5 into y=(-7/2)x to find y:
y = (-7/2)(1/5)
y = -7/10
So the solution to the system of equations is:
x = 1/5, y = -7/10