Answer:
Step-by-step explanation:
When using the substitution method we use the fact that if two expressions y and x are of equal value x=y, then x may replace y or vice versa in another expression without changing the value of the expression.
Solve the systems of equations using the substitution method
{y=2x+4
{y=3x+2
We substitute the y in the top equation with the expression for the second equation:
2x+4 = 3x+2
4−2 = 3x−2
2=== = x
To determine the y-value, we may proceed by inserting our x-value in any of the equations. We select the first equation:
y= 2x + 4
We plug in x=2 and get
y= 2⋅2+4 = 8
The elimination method requires us to add or subtract the equations in order to eliminate either x or y, often one may not proceed with the addition directly without first multiplying either the first or second equation by some value.
Example:
2x−2y = 8
x+y = 1
We now wish to add the two equations but it will not result in either x or y being eliminated. Therefore we must multiply the second equation by 2 on both sides and get:
2x−2y = 8
2x+2y = 2
Now we attempt to add our system of equations. We commence with the x-terms on the left, and the y-terms thereafter and finally with the numbers on the right side:
(2x+2x) + (−2y+2y) = 8+2
The y-terms have now been eliminated and we now have an equation with only one variable:
4x = 10
x= 10/4 =2.5
Thereafter, in order to determine the y-value we insert x=2.5 in one of the equations. We select the first:
2⋅2.5−2y = 8
5−8 = 2y
−3 =2y
−3/2 =y
y =-1.5
5.25 pounds of one alloy containing 45% copper and 36.75 pounds of 69% copper is used to make 42 pounds of 66% copper
<h3>What is an
equation?</h3>
An equation is an expression that shows the relationship between two or more variables and numbers.
Let x represent the amount of 45% copper and y represent the amount of 66% copper needed to make 42 pounds of a third alloy containing 66% copper. Hence:
x + y = 42 (1)
Also:
0.45x + 0.69y = 42(0.66) (2)
This gives:
x = 5.25, y = 36.75
5.25 pounds of one alloy containing 45% copper and 36.75 pounds of 69% copper is used to make 42 pounds of 66% copper
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Answer:
y=[-2]x[+][5]
Step-by-step explanation:
m= -2
Using the point (1,3) Find the value of b
3= -2(1)+b
3= -2+b
+2 +2
---------
5=b
y= -2x+5
B. 1/4(n - 64)
Multiplying n and -64 by 1/4 leaves you with 1/4n - 16, the original equation.
