5.2a - Equal values method

5.2a - Equal values method of solving systems of equations

Equal values method

Use this method when both of your equations are in the form of y=mx+b.

Take the equations and set them equal to each other and then solve for x.

Solve for x.

x = 1

Plug x into one of the original equations to solve for y.

y = 4

Put the x-value and y-value together into an ordered pair. This is the solution!

x = 1

y = 4

If you graphed the 2 lines, they would cross at (1,4).

Multiple Choice

True or false, you can use the Equal Values method to solve this problem?

 $y=-6x+4$  

 $-2x+y=-4$  

• True

• False

Multiple Choice

True or false, you can use the Equal Values method to solve this problem?

 $y=-6x+4$  

 $y=2x-4$  

• True

• False

Multiple Choice

Solve this system of equations for x.

 $y=-6x+4$  

 $y=2x-4$  

• x = 0

• x = 1

• x = 2

Multiple Choice

Take your x-value of 1 and plug it into one of these equations to solve for y.

 $y=-6x+4$  

 $y=2x-4$  

• y = 0

• y = -1

• y = -2

Multiple Choice

Now that you have your x-value of 1 and your y-value of -2, what is the solution to this system of equations?

 $y=-6x+4$  

 $y=2x-4$  

• (1,-2)

• (-2,1)

Multiple Choice

Solve this system of equations for x.

 $y=4x+4$  

 $y=x-2$  

• x = 2

• x = -2

• x = 1

Multiple Choice

Take your x-value of -2 and plug it into one of these equations to solve for y.

 $y=4x+4$  

 $y=x-2$  

• y = 4

• y = 0

• y = -4

Multiple Choice

Now that you have your x-value of -2 and your y-value of -4, put them together in an ordered pair.

 $y=4x+4$  

 $y=x-2$  

• (-4,-2)

• (-2,-4)

Special solutions

Sometimes, you will have linear equations that never cross (no solution) or are the same line (infinite solutions).

Multiple Choice

What is the solution to this systems of equations?

 $y=-2x-4$  

 $y=-2x+1$  

• No solution

• Infinite solutions

Multiple Choice

What is the solution to this systems of equations?

 $y=3x+7$  

 $y=3x+7$  

• No solution

• Infinite solutions