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EXPLANATION
The consecutive even numbers are
EXPLANATION
Let
be the first even number then, the next even number will be,
The difference of one-half the larger one and two-fifth the smaller one is 38 gives the equation,
We multiply through with an LCM of 10 to get,
This simplifies to,
We expand the brackets to get,
We group like terms to get,
This simplifies to
Therefore the next even number is is
The consecutive even numbers are
EXPLANATION
Let
be the first even number then, the next even number will be,
The difference of one-half the larger one and two-fifth the smaller one is 38 gives the equation,
We multiply through with an LCM of 10 to get,
This simplifies to,
We expand the brackets to get,
We group like terms to get,
This simplifies to
Therefore the next even number is is
Answer:
(a) (5, -3)
Step-by-step explanation:
The "substitution method" for solving a system of equations requires that you write an expression that can be substituted for a variable in one or more of the other equations in the system.
<h3>Expression to substitute</h3>The given equations are ...
- y = x -8
- 2x +3y = 1
We notice the first equation gives an expression for y. This is exactly what we want to substitute for y in the second equation.
<h3>Substitution</h3>When the expression (x-8) is substituted for y in the second equation, you get ...
2x +3(x -8) = 1
This simplifies to ...
5x -24 = 1
<h3>Solution</h3>This 2-step equation can now be solved in the usual way:
5x = 25 . . . . . . add 24 to isolate the variable term
x = 25/5 = 5 . . . . . divide by the coefficient of x
Note that we now know what the correct answer choice is.
Using the expression for y, we find ...
y = x -8 = 5 -8 = -3
The solution is (x, y) = (5, -3).
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The attached graph confirms this solution.
