Systems of Equations by Substitution

Systems of Equations by Substitution

System of Equations

• two or more linear equations

• solution is the intersection of the equations

Solutions:

• one solution

• no solution

• infinite number of solutions

Review: Graphing Systems of Equations

Multiple Choice

How many solutions does this system of equations have?

• One Solution
• No solution
• Infinitely Many Solutions
• Two Solutions

Multiple Choice

Where do these two lines intersect?

• No solution

• (-2, 3)

• (3, -2)

• (2, 3)

Multiple Choice

Where do these two lines intersect?

• No solution

• (-2, 3)

• (3, -2)

• (2, 3)

Steps for Solving Systems by Substitution

• Step #1 Isolate a variable in one of the equations to get an expression

• Steps #2 Substitute that expression (from step #1) into the other equation.

• Step #3 Solve for the intersection point (x , y).

• step #4 write your answer as an order pair (x, y).

Multiple Choice

What is the first step in solving a system by Substitution?

• Make sure both equations are in standard form.

• Make sure at least one equation is solved for one variable.

• Make sure both equations are in slope-intercept form.

• Make sure both equations can be solved.

Multiple Choice

Solve this system of equations.

y = 2x + 1

y = 4x - 1

• (1,3)

• (-1,-3)

• (-1,3)

• (3,1)

Multiple Choice

Use substitution to find the solution to the system of equations.

• (6,3)

• (-3,-6)

• (3,6)

• (-6,3)

Open Ended

Use substitution to find the solution to the system of equations.

Multiple Choice

y = -2x + 18
y = 8

• (5, 8)
• (-5, 8)
• (2, 8)
• (-2, 8)

Multiple Choice

Solve the following system:

 $y=-2$  

 $4x-3y=18$  

•  $\left(3,\ -2\right)$  

•  $\left(3,\ 2\right)$  

•  $\left(-2,3\right)$  

•  $\left(2,\ 3\right)$  

Try These:

Though the following questions are multiple choice, you should work them out on paper and upload your work to my email.

Multiple Choice

Solve for x and y
y = 2x + 1
y = 4x - 1

• (1,3)
• (-1,-3)
• (-1,3)
• (3,1)

Multiple Choice

x + 2y = 2

x = -4y + 2

• (-3, 0)

• (0, 2)

• (-3, -2)

• (2, 0)

Multiple Choice

x + 2y = 2

x = -4y + 2

• (-3, 0)

• (0, 2)

• (-3, -2)

• (2, 0)