Systems of Linear Equations

Solve for x and y
3x + 2y = 16
7x + y = 19

• (-2,5)

• (-2,-5)

• (2,-5)

• (2,5)

What are systems of linear equations?

• set of two or more linear equations in the same variables

• polynomial with three terms

• set of two or more linear inequalities in the same variables

How many solutions will this system have? 

• No solution

• One Solution

• I Don't Know

• Infinitely Many Solutions

If a system of linear equations has one solution, what does this mean about the two lines? 

• Parallel lines

• the same line 

• Intersecting lines

Enter the x coordinate of the solution to this system of equations. HINT: Make sure both equations are in (y=mx+b) form. Then do the shortcut with DESMOS

Mathematical Equivalence

ON

Enter the x coordinate of the solution to this system of equations. HINT: Make sure both equations are in (x + y = #) form. Then do the shortcut.

Mathematical Equivalence

ON

HINT: MAKE A TABLE FOR BOTH GYMS KEEPING TRACK OF THE TOTAL AMOUNT SPENT. THEN COUNT HOW MANY MONTHS IT TAKES BEFORE THEY BOTH SPEND THE SAME TOTAL.

Mathematical Equivalence

OFF

Solve the following system of equations by graphing:

• Infinite solutions

• (2, -2)

• (1, 0)

• (3, -4)

Solve the following system of equations using the elimination method:

• (-2, 1)

• no solutions

• (-2, 0)

• (-1, -3)