By substitution, the solution of the system of equations, 4x + 2y = 7 and y = 5x, is (1/2 , 5/2).
A system of linear equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.
There are three methods that can be used to solve system of linear equations.
1. Elimination
2. Substitution
3. Graphing
Using substitution method, given two linear equations in x and y,
4x + 2y = 7 (equation 1)
y = 5x (equation 2)
Since the second equation is already expressed in y in terms of x, substitute the second equation to the first equation.
4x + 2y = 7 (equation 1)
4x + 2(5x) = 7
4x + 10x = 7
Combining all terms containing the variable x on one side and the constants on the other side of the equality, and solving for x.
4x + 10x = 7
14x = 7
x = 1/2
Substitute the value of x in the second equation and solve for y.
y = 5x
y = 5(1/2)
y = 5/2
Hence, the solution of the given system of equations is (1/2 , 5/2).
To learn more about solving systems of equations: brainly.com/question/25869125
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C = 2*pi*r
So, C = pi*d
106.76 = pi*d
106.76/pi = d
d = ~33.98
Answer:B At least 4 pounds but less than 6 pounds.
Step-by-step explanation:
Answer:
22-9=16
so,
22-9
is 16
then you would take
16=16
so, you would have to divide the 2 numbers
then 1 is your answer
Step-by-step explanation:
Answer:
The number of bananas that Emily bought was 6 and the number of peaches that Emily bought was 8
Step-by-step explanation:
<u><em>The complete question is</em></u>
Emily and her children went into a grocery store and she bought $20.80 worth of bananas and peaches. Each banana costs $0.80 and each peach costs $2. She bought a total of 14 peaches and bananas altogether. Determine the number of peaches and the number of bananas that Emily bought
Let
x ----> the number of bananas that Emily bought
y ----> the number of peaches that Emily bought
we know that
She bought a total of 14 bananas and peaches altogether
so
-----> equation A
She bought $20.80 worth of bananas and peaches
so
-----> equation B
Solve the system by graphing
Remember that the solution is the intersection point both graphs
using a graphing tool
The solution is the point (6,8)
see the attached figure
therefore
The number of bananas that Emily bought was 6 and the number of peaches that Emily bought was 8
