Question

kuta software - infinite algebra 1
solving systems of equations by substitution
solve each system by substitution.
1)
① ( y = 6x - 11 )
② ( -2x - 3y = -7 )

1. ( 2x - 3y = -1 )

( y = x - 1 )

1. ( y = -3x + 5 )

( 5x - 4y = -3 )

1. ( -3x - 3y = 3 )

( y = -5x - 17 )

Explanation:

Let's solve problem 3: \( y = -3x + 5 \) and \( 5x - 4y = -3 \) using substitution.

Step 1: Substitute \( y \) into the second equation

We know \( y = -3x + 5 \), so substitute this into \( 5x - 4y = -3 \).
\( 5x - 4(-3x + 5) = -3 \)

Step 2: Simplify and solve for \( x \)

First, distribute the -4:
\( 5x + 12x - 20 = -3 \)
Combine like terms:
\( 17x - 20 = -3 \)
Add 20 to both sides:
\( 17x = 17 \)
Divide both sides by 17:
\( x = 1 \)

Step 3: Substitute \( x = 1 \) back into \( y = -3x + 5 \)

\( y = -3(1) + 5 \)
\( y = -3 + 5 \)
\( y = 2 \)

Answer:

The solution to the system is \( x = 1 \), \( y = 2 \) or \( (1, 2) \)