can some one help me with 2 problems thanks. y=1/2x+1,y=-3x+8, and y=1/2x+2, y=-x+5. show the work maybe i can figure it out some how.
Of course! I can help you solve these two problems.
Let's start with the first problem:
1) y = (1/2)x + 1
y = -3x + 8
To find the solution, let's equate the two expressions for y:
(1/2)x + 1 = -3x + 8
We can simplify the equation by multiplying each term by 2 to eliminate the fractions:
x + 2 = -6x + 16
Next, let's isolate the x term by moving all the x terms to one side of the equation:
x + 6x = 16 - 2
Combining like terms,
7x = 14
Now, divide both sides of the equation by 7 to solve for x:
x = 14/7
Simplifying,
x = 2
To find the corresponding value of y, substitute this value of x back into either of the original equations:
y = (1/2)(2) + 1
y = 1 + 1
y = 2
Therefore, the solution to the first problem is x = 2, y = 2.
Now, let's move on to the second problem:
2) y = (1/2)x + 2
y = -x + 5
Again, let's equate the two expressions for y:
(1/2)x + 2 = -x + 5
To eliminate the fractions, we can multiply each term by 2:
x + 4 = -2x + 10
Next, let's isolate the x term:
x + 2x = 10 - 4
Combining like terms,
3x = 6
Divide both sides of the equation by 3:
x = 6/3
Simplifying,
x = 2
Substitute this value back into either of the original equations to find the corresponding y value:
y = (1/2)(2) + 2
y = 1 + 2
y = 3
Therefore, the solution to the second problem is x = 2, y = 3.
I hope this step-by-step explanation helps you understand the process. Let me know if you have any further questions!