Combination method: add the two equations together
5) <span>4x-9y=1 6) 3x - 2y = 14
+( - 4x+6y=-2 ) + (2x + 2y = 6)
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0 - 5y = -1 5x + 0 = 20
-5y = -1 5x = 20
isolate the y isolate the x
-5y / -5 = -1/-5 5x/5 = 20/5
y = 1/5 x = 4
</span>4x-9y=1 3x - 2y = 14
4x - 9(1/5) = 1 3(4) - 2y = 14
4x - 9/5 = 1 12 - 2y = 14
4x - 9/5 (+9/5) = 1 (+9/5) 12 (-12) - 2y = 14 (-12)
4x = 14/5 -2y = 2
4x/4 = 14/5(/4) -2y(/-2) = 2(/-2)
x = 14/20 y = -1
Elimination method
7) 4x + 3y = 29 + (5x + 2y = 24)
eliminate one of the variables by multiply the number to both sides
2 (4x + 3y = 29) + 3 (5x + 2y = 24)
8x + 6y = 58
-( 15x + 6y = 72)
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-7x = - 14
-7x/-7 = -14/-7
x = 2
4(x) + 3y = 29
4(2) + 3y = 29
3y + 8 = 29
3y + 8 (-8) = 29 (-8)
3y = 21
3y/3 = 21/3
y = 7
8) like #7, you must eliminate one of the variables by multiply the number to both sides
-4x - 2y = 14
-10x + 7y = -25
7(-4x - 2y = 14)
-2(-10x + 7y = -25)
-28x - 14y = 98
- (20x -14y = -25)
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-48x = 123
-48x/-48 = 123/-48
x = -2.56
-4(-2.56) - 2y = 14
10.24 - 2y = 14
10.24(-10.24) - 2y = 14 (-10.24)
-2y = 3.76
-2y/-2 = 3.76/-2
y = -1.88
hope this helps
Answer:
Hey 2923928 !
<u>Answer</u><u>:</u><u> </u><u>The</u><u> </u><u>second</u><u> </u><u>choice</u>
• from distributive property;
• simplify:
Answer:
slope stays same for all parallel lines
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
2x-3=7
Add 3 to both sides:
2x=10
Divide both sides by 2:
x=5
Hope this helps!
The total of 2 buckets of popcorn and 3 boxes of candy would be $23.25
To answer this question you need to form a set of simultaneous equations and solve them. We can do this by saying that a bucket of popcorn = P, and a box of candy = C. Then we can say:
4P + 6C = 46.50
P + C = 9.75
There are then two possible ways to solve; you can either say that C = 9.75 - P using the second equation and then substitute it into the first, or you can multiply the second equation by either 4 or 6 to cancel out P or C.
I’m going to multiply the second equation by 4:
4P + 4C = 39
Now we can subtract this for, the first equation:
4P + 6C = 46.50
4P + 4C = 39
2C = 7.50
C = 3.75
Now we can substitute this value of C into one of the equations to find P:
P + C = 9.75
P + 3.75 = 9.75
P = 6
And now to answer the question, you just multiply P by 2 and C by 3 and add them together, which gives you $23.25
I hope this helps! Let me know if you have any questions :)
