Solving Systems of Equations

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8-2: Solving Systems of Equations using Substitution

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Presentation transcript:

Solving Systems of Equations By Substitution (Part 1)

Find the equation with an isolated letter y = x + 9 x + y = 3 Step 1 Find the equation with an isolated letter

(This is substitution) y = x + 9 x + y = 3 Step 2 Replace the right side of that equation whenever you see that letter in the other equation (This is substitution)

(This is substitution) y = x + 9 x + (x + 9) = 3 Step 2 Replace the right side of that equation whenever you see that letter in the other equation (This is substitution)

Simplify by rainbowing if you can x + (x + 9) = 3 Step 3 Simplify by rainbowing if you can

Simplify by rainbowing if you can x + x + 9 = 3 Step 3 Simplify by rainbowing if you can

x + x + 9 = 3 Step 4 Collect like terms

2x + 9 = 3 Step 4 Collect like terms

2x = 3 - 9 Step 4 Collect like terms

2x = -6 Step 4 Collect like terms

2x = -6 Step 5 Solve for the letter

2x = -6 2 2 Step 5 Solve for the letter

x = -3 Step 5 Solve for the letter

Now you know one of the variables! Don’t forget this step!!! x = -3 y = x + 9 ← Equation 1 x + y = 3 ← Equation 2 Step 6 Now you know one of the variables! Substitute this number into either one of the original equations to solve for the other variable.

Now you know one of the variables! Don’t forget this step!!! y = -3 + 9 Step 6 Now you know one of the variables! Substitute this number into either one of the original equations to solve for the other variable.

Now you know one of the variables! Don’t forget this step!!! y = 6 Step 6 Now you know one of the variables! Substitute this number into either one of the original equations to solve for the other variable.

Write your final answer as an ordered pair x = -3 y = 6 Step 7 Write your final answer as an ordered pair

Write your final answer as an ordered pair (-3, 6) Step 7 Write your final answer as an ordered pair

Check your answer using LS=RS (-3, 6) y = x + 9 Step 8 Check your answer using LS=RS

Check your answer using LS=RS 6 = -3 + 9 Step 8 Check your answer using LS=RS

Check your answer using LS=RS Yay! The left side equals the right side! My solution is correct 6 = 6 Step 8 Check your answer using LS=RS

Therefore, the solution to the system of equations y = x + 9 x + y = 3 is (-3, 6). If you were to graph both of these equations, this point is where the two lines would cross each other (the point of intersection).