Please, use parentheses to enclose each fraction:
y=3/4X+5 should be written as <span>y=(3/4)X+5
Let's eliminate the fraction 3/4 by multiplying the above equation through by 4:
4[y] = 4[(3/4)x + 5]
Then 4y = 3x + 20
(no fraction here)
Let 's now solve the system
4y=3x + 20
4x-3y=-1
We are to solve this system using subtraction. To accomplish this, multiply the first equation by 3 and the second equation by 4. Here's what happens:
12y = 9x + 60 (first equation)
16x-12y = -4, or -12y = -4 - 16x (second equation)
Then we have
12y = 9x + 60
-12y =-16x - 4
If we add here, 12y-12y becomes zero and we then have 0 = -7x + 56.
Solving this for x: 7x = 56; x=8
We were given equations
</span><span>y=3/4X+5
4x-3y=-1
We can subst. x=8 into either of these eqn's to find y. Let's try the first one:
y = (3/4)(8)+5 = 6+5=11
Then x=8 and y=11.
You should check this result. Subst. x=8 and y=11 into the second given equation. Is this equation now true?</span>
Your work appears to be correct.
The results from a graphing calculator are in agreement.
Assuming John does not get premium pay for hours over 40, his pay will be ...
... 43 hours × $9.00 = $387
... - 6.2% × $387 = $23.99
... - 1.45% × $387 = $5.61
... - $15.00
... - 5% × $387 = $19.35
... - 10% × ($387 -19.35) = $36.77
... = $286.28 . . . . net pay after all the deductions
Three and a half divided by seven-eighth equals seven over two times eight over seven equals fifty over fourteen equals four
5(2x+8)-5x=5(5x+6)
Distribute
10x+40-5x=25x+30
combine like terms
5x+40=25x+30
-5x -5x
subtract 5x from both sides
40=20x+30
-30 -30
subtract 30 from both sides
10=20x
÷20 ÷20
divide both sides by 20
1/2=x is your final answer
