MATHEMATICS MIDDLE SCHOOL

Solve the following equations 4x + 3y =17 3x + 2y = 13

Answers

Answer 1

Answer:

Answer:

(5,-1)

Step-by-step explanation:

4x+3y=17

3x+2y=13

So elimination sounds fun but we will have to do manipulation:

Multiply top equation by 2 and bottom equation by 3. This will cause the second term in both by 6y which means we would be setup for elimination.

8x+6y=34

9x+6y=39

--------------------now subtract the equations

-x+0=-5

So x=5

Now plug it into either question (no matter which-pick and choose)

I will go with the second original 3x+2y=13

So if x=5 we have 15+2y=13

Subtract 15 on both sides: 2y=-2

Now divide both sides by 2: y=-1

Answer (5,-1)

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Answers

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Are the ratios 3:1 and 16:4 equivalent

Answers

First, simplify the 16:4 ratio.
• 16:4 ÷ 2 = 8:2 ÷ 2 = 4:1

Now, check to see if they're equivalent:
• 3:1 = 4:1 ???
- 3:1 =/= 4:1

So, NO these ratios are not equivalent.

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Mixing 4 ml of red paint and 15 ml yellow paint makes orange paint. How much red would be needed if you use 100 ml of yellow paint? Please show work

Answers

$(4ml)/(15ml)=(xml)/(100ml)\n\ncross\ multiply\n\n15x=4*100\n\n15x=400\ \ \ \ |divide\ both\ sides\ by\ 15\n\nx=(400)/(15)\ \ \ \ \ |divide\ a\ numerator\ and\ a\ denominator\ by\ 5\n\nx=(80)/(3)\n\nx=26(2)/(3)\ (ml)\n\nAnswer:26(2)/(3)\ ml\ of\ red\ paint.$