A system of equations is a set of two or more equations with the same variables. Below are some examples of systems.
The solution of a system of equations in two variables is an
ordered pair that satisfies both equations.
One method for solving a system of equations is to graph the
equations on the same coordinate plane. The coordinates of the point of
intersection are the solution.
Solve each system of equations by graphing.
1. y = 2x
y
= –x + 3
Alternative Solutions:
The
graphs appear to intersect at (1, 2).
Check
this estimate by substituting the coordinates into each equation.
Check:
The
solution of the system of equations is (1, 2).
2. x – y = –2
x +
y = 4
Alternative Solutions:
The graphs appear to
intersect at (1,
3). Check this estimate.
The
solution of the system of equations is (1, 3).
A graphing calculator can be used to solve systems of
equations or to check solutions.
Sales
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3. The Math Club is selling T-shirts for a profit of $4 each and caps for a
profit of $5 each. The club wants to sell 50 items and make a profit of $230.
How many of each item should the club try to sell?
Alternative Solutions:
Let x
= the number of T-shirts and y = the number of caps. You can write
two equations to represent this situation.
Graph x
+ y = 50 and 4x + 5y = 230. The graphs appear to
intersect at (20, 30). Check this estimate.
Check:
They should
try to sell 20 T-shirts and 30 caps.
Sumber
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