Below is a puzzle that requires algebraic thinking. Choose two numbers to fill in the white boxes in the top row. Follow the arr
ows to add two numbers together. The goal is to end with a sum of 42. The puzzle is repeated to see if there is more than one solution. 1st Answer * How might you use algebra to determine your two numbers? 7 Your answer 2nd Answer * 42 How might you use algebra to determine your two numbers? 8
1 answer:
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The solution of the equation is and
Explanation:
The equations are and
First we shall solve the equation graphically.
The image of the graph is attached below.
This contains the solution to the system of equations.
The equations and
are plotted on the graph.
The intersection of these two equations are the solutions of the system of equations.
Thus, the intersection of the two equations are and
Now, we shall solve the equation algebraically.
Let us solve the equation using substitution method.
Let us substitute in
, we get,
Adding both sides by 2x, we have,
Adding both sides by 2, we get,
Dividing both sides by 3,
Thus, the value of x is 3.
Substituting in
, we get,
Thus, the value of y is 1.
Hence, The solution of the equation is and
