Question

do you know how? use substitution to solve each system of 5. $y = 6 - x$ $4x - 3y = -4$ 6. $x = -y + 3$ $3x - 2y = -1$ 7. $-3x - y = 7$ $x + 2y = 6$ 8. $6x - 3y = -6$ $y = 2x + 2$ 9. a sports store sells a total of 70 soccer ball

Explanation:

Let's solve problem 5 using substitution:

Step1: Substitute \( y = 6 - x \) into \( 4x - 3y = -4 \)

We have the second equation \( 4x - 3y = -4 \). Replace \( y \) with \( 6 - x \):
\( 4x - 3(6 - x) = -4 \)

Step2: Simplify and solve for \( x \)

Expand the left side: \( 4x - 18 + 3x = -4 \)
Combine like terms: \( 7x - 18 = -4 \)
Add 18 to both sides: \( 7x = -4 + 18 = 14 \)
Divide by 7: \( x = \frac{14}{7} = 2 \)

Step3: Substitute \( x = 2 \) into \( y = 6 - x \)

\( y = 6 - 2 = 4 \)

Step1: Substitute \( x = -y + 3 \) into \( 3x - 2y = -1 \)

The second equation is \( 3x - 2y = -1 \). Replace \( x \) with \( -y + 3 \):
\( 3(-y + 3) - 2y = -1 \)

Step2: Simplify and solve for \( y \)

Expand: \( -3y + 9 - 2y = -1 \)
Combine like terms: \( -5y + 9 = -1 \)
Subtract 9: \( -5y = -1 - 9 = -10 \)
Divide by -5: \( y = \frac{-10}{-5} = 2 \)

Step3: Substitute \( y = 2 \) into \( x = -y + 3 \)

\( x = -2 + 3 = 1 \)

Step1: Solve \( -3x - y = 7 \) for \( y \)

Add \( 3x \) to both sides: \( -y = 3x + 7 \)
Multiply by -1: \( y = -3x - 7 \)

Step2: Substitute \( y = -3x - 7 \) into \( x + 2y = 6 \)

\( x + 2(-3x - 7) = 6 \)

Step3: Simplify and solve for \( x \)

Expand: \( x - 6x - 14 = 6 \)
Combine like terms: \( -5x - 14 = 6 \)
Add 14: \( -5x = 6 + 14 = 20 \)
Divide by -5: \( x = \frac{20}{-5} = -4 \)

Step4: Substitute \( x = -4 \) into \( y = -3x - 7 \)

\( y = -3(-4) - 7 = 12 - 7 = 5 \)

Answer:

The solution to the system is \( x = 2 \), \( y = 4 \) (or the ordered pair \( (2, 4) \))

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Now problem 6: