Download Solving Systems of Equations – Part II

Solving Systems of Equations – Part II
HAND IN AT END OF PERIOD
Remember:
A system of equations is a set of two or more equations that are true at the same time. The equations are graphed
on the same coordinate plane.
The solution to the system of equations is the point whose ordered pair makes all the equations true. On a graph,
it is the point where the lines intersect.
3 Ways to solve systems of equations:
1. Graph the two equations and find the point of intersection.
2. Substitution
3. Elimination
Today’s objective: Solve systems of equations by substitution.
You can solve systems of equations by substitution:
Step 1: Solve an equation for either x or y. You get an algebraic expression.
Step 2: Substitute the algebraic expression for the variable in the other equation.
Solve for a numerical value.
Step 3: Substitute the numerical value you find and solve for the 2nd variable.
Example:
Equation 1: 3x + 2y = 4
Equation 2: 2x – y = 5
Step 1: Solve equation 2 for y:
2x – y = 5
-2x
-2x
-y = – 2x + 5
y = 2x – 5 (Get a positive y by
multiplying everything by -1)
Solution: x = 2; y = -1;
Step 2: Substitute 2x-5 for y in
equation 1:
3x + 2y
=4
3x + 2(2x – 5) = 4
3x + 4x – 10 = 4
7 x – 10 = 4
+10 +10
7x
= 14
x = 2
= 14
(2, -1) is the solution.
Step 3: Substitute 2
for x in equation 1:
3x + 2y = 4
3(2) + 2y = 4
6 + 2y = 4
-6
-6
2y = -2
Y = -1
X
2
Check: Plug in 2 and – 1 in each equation to check the =solution
3x + 2y = 4
2x – y = 5
3(2) + 2(-1) = 4
2(2) – (-1) = 5
6 - 2 = 4 True; checked
4 + 1 = 5 True; checked.
Further examples are given at this website:
https://www.khanacademy.org/math/algebra-basics/core-algebra-systems/core-algebra-systems-tutorial/v/solvinglinear-systems-by-substitution
Assignment: On loose leaf complete the following worksheet,
HAND IN ALL WORK AT THE END OF THE PERIOD.
Systems of Equations Substitution.
NO CREDIT GIVEN FOR WORK NOT HANDED IN AT END OF PERIOD.