<em>Replace all occurrences of x with y + 3 in each equation.</em>
<em>Replace all occurences of x in 6x - 5y = 15 with y + 3.</em>
<em>6 (y+3) -5y = 15</em>
<em>x = y + 3</em>
<em>Simplify 6 (y + 3) - 5y.</em>
<em>Simplify each term.</em>
<em>Apply the distributive property.</em>
<em>6y + 6 · 3 - 5y = 15</em>
<em>x = y + 3</em>
<em>Multiply 6 by 3.</em>
<em>6y + 18 - 5y = 15</em>
<em>x = y + 3</em>
<em>Subtract 5y from 6y.</em>
<em>y + 18 = 15</em>
<em>x = y + 3</em>
<em>Move all terms not containing y to the right side of the equation.</em>
<em>Subtract 18 from both sides of the equation.</em>
<em>y = 15 - 18</em>
<em>x = y + 3</em>
<em>Subtract 18 from 15.</em>
<em>y = -3</em>
<em>x = y + 3</em>
<em>Replace all occurences with y with -3 in each equation.</em>
<em>Replace all occurences of y in x = y + 3 with -3.</em>
<em>x = (-3) + 3</em>
<em>y = -3</em>
<em>Add -3 and 3.</em>
<em>x = 0</em>
<em>y = -3</em>
<em>The solution to the system is the complete set of ordered pairs that are valid solutions.</em>
<em>(0,-3)</em>
<em>The result can be shown in multiple forms.
</em>
<em>Point Form:</em>
<em>(0,-3)</em>
<em>Equation Form:</em>
<em>x = 0, y = -3</em>
I think the answer is C. 1,320
Using proportions, it is found that:
a) A raise of $500 would be equivalent to a percentage of 80%.
b) From the above percentage, it would fall into the Gold Award range.
<h3>What is a proportion?</h3>
A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using arithmetic operations such as multiplication and division.
One example of application of proportions is for percentage problems, as a percentage is given by the amount a divided by the total amount b, and multiplied by 100%.
The goal of the raise is of $625, hence b = 625, and considering a raise of $500, a = 500, hence the percentage of the raise is given as follows:
500/625 x 100% = 80%.
To find the range of the raise, we look at the table. For a percentage of 80%, the amount is a Gold Award contribution.
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By solving the given equation 20 + 0.44x = 19 + 1.69x we get x=0.8.
<h3>What is meant by an equation?</h3>
When two expressions are connected with the equals sign (=) in a mathematical formula, it expresses the equality of the two expressions. For instance, an equation in French is described as having one or more variables, whereas in English, an equation is any properly written formula that consists of two expressions linked by the equals sign.
Determine which values of the variables result in the equality to be true in order to solve an equation with variables. The values of the variables that must fulfill the equality to constitute the answer are known as the unknowns, together with the variables for which the equation must be solved.
Given,
20 + 0.44x = 19 + 1.69x
20-19=1.69x-0.44x
1=1.25x
x=0.8
Therefore, by solving the given equation 20 + 0.44x = 19 + 1.69x we get x=0.8.
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