Linear Systems Point of Intersection

Two graphs ________ if they have all their points in common. For example, the graphs of y = 2x + 4 and 3y = 6x + 12 ________: both graphs are lines with a slope of 2 and a y-intercept of 4. When the graphs of two equations ________, those equations share all the same solutions and have an infinite number of intersection points.

• Point of Intersections

• Systems of Equations

• Solution

• Coincide

A method for solving a system of equations. The key step in using the ___________________ is to add both sides of two equations to eliminate one of the variables. For example, the two equations in the system below can be added together to get the simplified result 7x = 14.

• Systems of Equations

• Point of Intersection

• Elimination Method

• Solution

A method for solving a system of equations by replacing one variable with an expression involving the remaining variable(s). For example, in the system of equations above, the first equation tells you that y is equal to –3x + 5. We can substitute –3x + 5 in for y in the second equation to get 2(–3x + 5) + 10x = 18, then solve this equation to find x.

• Point of Intersection

• Elimination Method

• Solution

• Substitution Method

Find the solution to the system of equations.

5x + 4y= −14

y =  −7x  −  15 

• (-2, -1)

• (1, -2)

• (-2, 1)

• (-1, -2)

Tags

A1.AREI.6

The solution of a system of linear equations is...

• the y-intercept (b)

• the intersection of the two equations on a graph

• the second equations' answers

• the slope (m)

What is the solution to this system of equations?

• (4, -1)

• (-1, 4)

• (-4, 1)

• (-4, -1)

What is the solution to this system?

• (3, -1)

• (2, -6)

• No Solution

• (6, -2)

What is the solution to this system?

• (-3, -8)

• (-8, -3)

• (3, -8)

• (8, 3)

How many solutions will this system have? 

• No solution

• One Solution

• I Don't Know

• Infinitely Many Solutions

Solve the system given:
3x - y = 7
2x + y = 3

• (-1,2)

• (5,4)

• (4,5)

• (2,-1)