Systems of Equations - using Substitution Method

Solve this system by substitution.

Remember just substitute (4x) in for y in

6x - 4y = -10.

Now you should have the following written on your paper.

6x - 4(4x) = -10

Solve for "x" and then use that x-value to find the y.

• (1, -4)

• (1, 4)

• (-4, -7)

• (-7, -4)

What is the solution to this system of equations?

A solution to the system is the one (x,y) pair that both graphs have in common. That would be where the two graphs intersect.

• (4, -1)

• (-1, 4)

• (-4, 1)

• (-4, -1)

A system of equations will have Infinite solutions if.....

• They are parallel lines.

• One has a negative slope and the other has a negative slope.

• They are the exact same line.

• Their graphs intersect at one location.

How many solutions will this system have?

• No solution

• One Solution

• I Don't Know

• Infinitely Many Solutions

Is (1,10) a solution to this system? (HINT: It should satisfy or make both equations True if it is.)

y=7x+5

y=x+9

• yes

• no

Solve the following systems of equations using substitution:

2y + x = -15

x = 3y

Substitute (3y) in for (x) in the first equation: 2y + (3y) = -15

Now solve for y. Then use the value of y to find x.

• (-3, -9)

• (-9, -3)

• (-3, 9)

• (9, -3)

y = -2x + 18

y = 8

Substitute (8) in for (y) in the first equation!

Then you will have 8 = -2x + 18

Now solve for x.

• (5, 8)

• (-5, 8)

• (2, 8)

• (-2, 8)

Solve this system of equations.

y = 2x + 1

y = 4x - 1

When both are in slope intercept form just set both expressions that are equal to y equal to each other OR you could work in BACKWARDS by just plugging in the four (x,y) pairs and see which one makes BOTH equations TRUE.

• (1,-3)

• (1,3)

• (-1,3)

• (3,1)

x + 2y = 2

x = -4y + 2

One of the equations already has x isolated.

What will the first equation look like after you

substitute (-4y + 2) into the first equation for x.

• x + 2y - 4y +2 = 2

• x = x + 2y

• (-4y + 2) + 2y = 2

• 2y = -4y + 2

7x + y = -20

y = 3x + 10

What will an equation look like after you substitute

y = (3x + 10) into the first equation?

• 7x + 10 = -20

• 7x + (3x + 10) = -20

• 7(3x + 10) + y = -20

• y = 3(7x + y) + 10 = -20