Question

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systems of equations
in the last activity, you began exploring how to find a solution that works for two different linear functions.
this is called a system of equations.
a system of equations is when two or more equations share the same variables. a solution to that system
has to be true for all the equations, not just one.
think back to the last activity when we graphed two lines on the same coordinate plane. the green line
represents the number pairs that had a difference of 8. the purple line represents the number pairs with a
sum of 1.

1. where did you see the solution to the system of equations on the graph?
2. how can you test if that point is a solution to both equations in the system?
3. tatiana starts with $8 in her piggy bank and saves $2 per week. julian starts with $0 in his

piggy bank and saves $4 per week.
a. write an equation to model how much money tatiana has in her piggy bank after x weeks.
b. write an equation to model how much money julian has in his piggy bank after x weeks.
last updated 9/15/21

Explanation:

Step1: Answer graph solution location

The solution is at the intersection point of the two lines on the graph, which is $(3, -4)$.

Step2: Explain solution testing method

Substitute the $x$ and $y$ values of the point into both linear equations. If both equations are true (both sides are equal) after substitution, the point is a solution.

Step3: Model Tatiana's savings

Let $y_T$ = total money, $x$ = weeks. Initial amount is $8$, weekly save $2$.
$y_T = 2x + 8$

Step4: Model Julian's savings

Let $y_J$ = total money, $x$ = weeks. Initial amount is $0$, weekly save $4$.
$y_J = 4x$

Answer:

1. The solution is at the point where the two lines intersect, which is $(3, -4)$.
2. Substitute the $x$ and $y$ coordinates of the point into each equation in the system. If both equations are satisfied (both sides of each equation are equal after substitution), then the point is a solution to the system.
3. a. $y = 2x + 8$

b. $y = 4x$