Practice solving systems by graphing

1.) 2.) 2x + 5y = –5

x + 3y = 3

Solving systems of linear equations by substitution.

EXAMPLE 1 Use the substitution method

Solve the system using the substitution method.

2x + 5y = –5

x + 3y = 3

Equation 1

Equation 2

SOLUTION

STEP 1 Solve Equation 2 for x.

x = –3y + 3 Revised Equation 2

x + 3y = 3 -3y -3y

EXAMPLE 1 Use the substitution method

STEP 2Substitute the expression for x into Equation 1 and solve for y.

2x +5y = –52(–3y + 3) + 5y = –5

y = 11

Write Equation 1.

Substitute –3y + 3 for x.

Solve for y.STEP 3

Substitute the value of y into revised Equation 2 and solve for x.

x = –3y + 3

x = –3(11) + 3

x = –30

Write revised Equation 2.

Substitute 11 for y.

Simplify.

-6y + 6 + 5y = -5 -y +6 = -5 -y = -11

STEP 4

STEP 5

EXAMPLE 1 Use the substitution method

CHECK Check the solution by substituting into the original equations.

2(–30) + 5(11) –5=? Substitute for x and y. =? –30 + 3(11) 3

Solution checks. 3 = 3 –5 = –5

The solution is (– 30, 11).

ANSWER

EXAMPLE 2 Use the substitution method

Solve the system using the substitution method.

3x - y = 2

6x + 3y = 14

Equation 1

Equation 2

SOLUTION

STEP 1 Solve Equation 1 for y.

y = 3x – 2 Revised Equation 1

3x - y = 2 -3x -3x

-y = 2 – 3x

-1 -1 -1This is what happens if you don’t do your math

EXAMPLE 2 Use the substitution method

STEP 2Substitute the expression for y into Equation 2 and solve for x.

6x +3y = 14 6x + 3(3x – 2) = 14

x = 4/3

Write Equation 2.

Substitute 3x – 2 for y.

Solve for y.

STEP 3

Substitute the value of y into revised Equation 2 and solve for x.

y = 3x – 2

y = 3(4/3) – 2

y = 2

Write revised Equation 1.

Substitute 4/3 for x.

Simplify.

6x + 9x – 6 = 14 15x – 6 = 14 15x = 20

STEP 4

STEP 5

Distribute , combine like terms, and solve.

EXAMPLE 3 Use the substitution method

Solve the system using the substitution method.

x - 2y = 4

3x - 6y = 8

Equation 1

Equation 2

SOLUTION

STEP 1 Solve Equation 1 for x.

x = 2y + 4 Revised Equation 1

x - 2y = 4 +2y +2y

EXAMPLE 3 Use the substitution method

STEP 2Substitute the expression for x into Equation 2 and solve for y.

3x - 6y = 8 3(2y + 4) - 6y = 8

The y canceled out

Write Equation 2.

Substitute 2y + 4 for x.

Solve for y.STEP 3

6y + 12 - 6y = 8 12 = 8

When this happens and your final answer is false 12 ≠ 8 the answer is NO Solution.

What if the final answer had been true?

The answer would have been infinite solutions.

You try solving by substitution.3.) 4.)