Substitution method is used to solve the linear system of equations for one or more variables.
Consider the first equation y = 3x + 3 -----(1)
In equation (1) plug in y=x-1, we get
x -1 = 3x + 3
Add -3x on both side , we get
x-3x -1 = 3x-3x +3
-2x-1=0 + 3
Now add +1 on both sides, we get
-2x-1+1= 3+1
-2x + 0 =4
Now divide both side by -2
-2x/-2= 4/-2
X= -2
Now put x=-2 in the the second equation,
y=x-1
y=(-2)-1
y=-3
Solution(-2,-3)
Answer:
1/2.
Step-by-step explanation:
The slope = rise/run
= (-13 - (-10)) / (3 - 9)
= -3 / - 6
= 1/2.
Answer:
x => y
0 => 0
2 => 3
4 => 6
-2 => -3
Step-by-step explanation:
The equation of a proportional relationship is represented as y = kx,
where, k = y/x
We are given that k = ³/2
This means that, equation of the relationship therefore would be:
y = ³/2x
Use this equation to solve for each missing value on the table given:
✔️Where, y = 0, substitute y = 0 into y = ³/2x to find x:
0 = ³/2x
0 * 2 = 3x
0 = 3x
0/3 = x
x = 0
✔️Where, x = 2, substitute x = 2 into y = ³/2x to find y:
y = ³/2(2)
y = 3
✔️Where, y = 6, substitute y = 6 into y = ³/2x to find x:
6 = ³/2x
6 * 2 = 3x
12 = 3x
12/3 = x
x = 4
✔️Where, x = -2, substitute x = -2 into y = ³/2x to find y:
y = ³/2(-2)
y = -3
Answer: 20% increase
Step-by-step explanation:
change/ original number
(60 - 50 / 50) x 100 = 20
20%
9514 1404 393
Answer:
18
Step-by-step explanation:
90 = 18·5
126 = 18·7
180 = 18·10
990 = 18·55
The greatest common factor of these numbers is 18.
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<em>Comment on the GCF</em>
It can be useful to know Euclid's algorithm for finding the GCF:
- Determine the remainder from dividing the larger number by the smaller.
- If the remainder is zero, the smaller number is the GCF. If the remainder is non-zero, use it to replace the larger number and repeat from step 1.
For example, 126 mod 90 = 36; 90 mod 36 = 18; 36 mod 18 = 0, so 18 is the GCF of 126 and 90. (The modulo function 'mod' returns the remainder from division.)
