Systems by Substitution

Solve the following multi-step equation on paper, then answer the following questions to explain your work.

3x-2(-4+5x)=-20

What is your first step?

• Distribute a 2 to -4+ 5x, which equals -8+10x

• Distribute a -2 to -4+ 5x, which equals -8+10x

• Distribute a 2 to -4+ 5x, which equals 8-10x

• Distribute a -2 to -4+ 5x, which equals 8-10x

Your first step should have been to distribute a -2.

Our new equation is 3x+8-10x =-20

What is your next step?

• Combine like terms 3x and -10x to get -7x

• Combine like terms 3x and 8 to get 11x

• Zero pair -20 by adding 20 to both sides

• Combine like terms 3x and 10x to get 13x

After combining like terms, our new equation is -7x+8=-20

Now we have a two step equation. What should your next step be ?

• Create a zero pair to remove the +8 by subtracting 8 from both sides

• Create a zero pair to remove the 8 by adding 8 to both sides

• Create a zero pair to remove the -7x by adding 7x to both sides

• Create a zero pair to remove the -20 by adding 20 to both sides

Our new equation is -7x=-28

Our final step is to divide by the coefficient to get 1x.

What did you divide by to get 1x?

• 7

• 7x

• -7

• -7x

Now that we have 1x, we know the solution to the multi-step equation.

What is your solution?

• X=28

• X=7

• X=4

• X=-28/7

Solve the following system of linear equations by substitution on paper, then answer the following questions to explain your work!

What is the 1st step?

• Combine like terms

• Substitute for my variable

• Make sure at least one equation is in slope intercept-form.

Which equation is in slope intercept form?

• Top equation: y=2x+11

• Bottom equation: 3x+2y=1

With one equation in slope intercept form, what is the 2nd step?

• Convert the bottom equation into slope-intercept form.

• Substitute 2x+11 into the second equation for y

• Substitute 2x+11 into the second equation for x

• Substitute 3x+2y into the first equation equation for y

You should have substituted the 2x+11 into the second equation for the variable y.

What is the next step?

• combine like terms 3x+2x

• distribute 2 with 2x+11

After distributing the 2, you have the multi-step equation:

3x+4x+22=1

What should you do next?

• Combine like terms 3x and 22

• Combine like terms 3x and 4x

• zero pair 3x

• Isolate the x