Question

learn it
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.

Explanation:

1. For a system of linear equations graphed on a coordinate plane, the solution is the point that satisfies both equations, which corresponds to where the two lines intersect.
2. To verify a point is a solution, substitute its x and y values into each equation of the system. If both equations remain true (both sides are equal) after substitution, the point is a valid solution.

3a. Tatiana's total savings follow a linear model: initial amount plus weekly savings multiplied by the number of weeks.
3b. Julian's total savings follow a linear model: weekly savings multiplied by the number of weeks (since he has no initial amount).

Answer:

1. The solution is at the intersection point of the two lines on the graph.
2. Substitute the point's x and y values into each equation in the system. If both equations are satisfied (both sides are equal), the point is a solution.

3a. $y = 2x + 8$
3b. $y = 4x$