Linear Systems Different Methods

Solve the given system of linear equations:

Answer explanation

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

What are the steps in solving for the solution to a system of linear equations in two variables using the elimination method.

Answer explanation

5 STEPS IN SOLVING SYSTEM OF LINEAR EQUATIONS BY ELIMINATION METHOD

STEP 1:

Multiply, if necessary, one or both equations by a constant so at least one pair of like terms has the same or opposite coefficients.

STEP 2:

Add or subtract the equations to eliminate one of the variables.

STEP 3:

Solve the resulting equation.

STEP 4:

Substitute the value from Step 3 into one of the original equations and solve the other variable.

STEP 5:

Check your answer in the other equation you did not use in Step 4.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Why is it important to know different methods in solving a system of linear equations? What could possibly happen if you only know one way of solving?

Answer explanation

Knowing different methods to solve a system of linear equations allows flexibility in tackling various problems. Relying on one method may lead to difficulties with complex systems or specific cases where that method is inefficient.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Solve the following system of linear equations:

Answer explanation

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

• No Solution

• (2, 2)

• (-1, 2)

• (-1, -2)

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

When you graph the exact same equation twice,

• you will have no solution. 

• you will have one solution.

• you will have infinite solutions. 

• you will graph a giraffe. 

Tags

CCSS.8.EE.C.8B

Does the system have one, none or infinite solutions?
8x + 4y = 12
y = -2x + 3

• (0,3)

• (3,0)

• No solution(parallel lines)

• Infinitely many solutions

Tags

CCSS.8.EE.C.8B

• Infinite number of solutions

• (0, 7)

• (-5, -7)

• (5, 7)

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

(3, -6)

(3, -8)

Infinite number of solutions

(3, 6)

• (3, -6)

• (3, -8)

• Infinite number of solutions

• (3, 6)

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

7x + 4y = -6
-7x - 6y = 30
answers in (x,y)

• (6, -12)

• (6, 12)

• (-12, 8)

• (12, -8)

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6