Solve the system of equations.6x – 3y = 3
–2x + 6y = 14
What number would you multiply the second equation by in order to eliminate the x-terms when adding to the first equation?
What number would you multiply the first equation by in order to eliminate the y-terms when adding to the second equation?
Answers
Keywords:
Systems of equations, variables, values, steps
For this case we have a system of two equations with two variables given by "x" and "y" respectively. We must solve the system by finding the values of the variables. For this, we follow the steps below:
Step 1:
We multiply the second equation by 3:
Step 2:
We add both equations:
Step 3:
We substitute in the first equation:
Thus, the solution of the system is given by
Answer:
The second equation must be multiplied by "3" to eliminate the terms of the "x" when added with the first equation
The first equation must be multiplied by "2" to eliminate the terms of the "y" when added with the second equation
The system solution is given by
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Answers
Answer:
Find the slope of the original line and use the point-slope formula
y−y1=m(x−x1) to find the line parallel to y=2x−7. y=2x+12
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Answer:
y= -1/2x
Step-by-step explanation:
Equation of the line is always in the form y=mx + c
where c is the y-intercept ( where the graph crosses the y-axis) and m is the gradient.
The straight line passes through the origin which are the points (0,0) hence
gradient= change in y÷ change in x
G= -2-0 ÷ 4-0 =-2÷4= -1/2x
y= 1/2x+c
-2=-1/2(4)+c
-2=-2+c
-2+2=c
c=0
∴ the equation of the line is y=-1/2x
Final answer:
The equation of the line passing through the origin and the point A(4,-2) is y = -0.5x.
Explanation:
In Mathematics, the equation of the line can be found using the point-slope form which is y = mx + c, where 'm' is the slope of the line and 'c' is the y-intercept. Since the line passes through the origin O(0,0), the y-intercept 'c' is 0. The slope 'm' of the line is found by the formula 'change in y/change in x'. Given the point A(4,-2), the change in y (the difference in the y-values of your two points) is -2 - 0 = -2, and the change in x (the difference in the x-values of your two points) is 4 - 0 = 4. Therefore, the slope 'm' is -2/4 = -0.5.
Substitute 'm' and 'c' values in the equation y = mx + c, we get the equation of the line OA as y = -0.5x.
Learn more about Equation of a Line here:
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The factors of 65 are 1, 5, 13, and 65 .
The factors of 70 are 1, 2, 5, 7, 10, 14, 35, and 70 .
The factors of 65 are 1,5, 13,65 because all of these can divide 65 without leaving any remainder
The factors of 70 are 1,2,5,7,10,14,35,70 since all of them can divide 70 without leaving any remainder
The factors of 100 are 1,2,4,5,10,20,25,50,100 since all these can divide 100 without leaving any remaider
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Simplify by dividing both sides by 5
1/7
Final Answer: 1/7
b. What do the slope and S-intercept of the graph of the relation represent, base on the interpretation from part a.?
c. If Tim plans to stop his savings once he has accumulated $1250, what are the domain and range of this relation.
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Answer:
Step-by-step explanation:
Given that Tim has developed a money saving strategy that uses the formula S=450+100r.
a) 450 will be savings always and for every r an additional 100 would be saved
b) Slope = 100 represents the increase of S for a unit increase of 1.
S intercept = 450 is the savings even when r=0
c) Since max savings is 1250 and min is 450
Range = (450,1250)
For 450 range, domain r =0 and for range 1250, domain r = 8
Domain =(0,8)
B) The Slope represents the time it takes to make 100 dollars, and S represents the total amount of money Tim has.
C) If Tim got to 1250 dollars, it would be 8 for R. So 8 would be the domain and 1250 for the range.