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 ...
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.
Since the function f(x) is written in the form y = mx + b, where m is the slope and b is the y-intercept, it currently has a y-intercept of b = 6. If this function is shifted downwards (vertically) by 12 units, its new y-intercept will be:
The triangle in the right side of the first row, the triangle in the left side of the second row and the triangle in the left side of the third row are labeled correctly.
<h3>What triangles are represented correctly?</h3>
Triangles can be defined in terms of their base and their height. Both are linear measures. The base is one side of the triangle and the height is a line perpendicular to the base that meets the vertex opposite to the base.
Based on this explanation we find that the triangle on the right of the first row, the triangle on the left of the second row and the triangle on the left of the third row are labelled correctly.
To learn more on representation of triangles: brainly.com/question/18884053
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We can determine that there are two types of soup: one can costing $0.54, and the other costing $0.34. 5 cans of the $0.54 soup would cost a total of $2.70, while 5 cans of the $0.34 soup would cost $1.70. Therefore, the combined cost of all 10 cans of soup, being 5 of each type, is $4.40.
