Answered

Spring 2024
Algebra 1
Final Exam Study Guide
Directions: Complete the questions below. DUE: Tuesday, June 4th
Chapter 5 System of Linear Equations
1. Solve the system of equations by using SUBSTITUTION. Provide your answer in coordi
y= -2x-9
6x-5y=-19
2. x = 6y-7
4x+y=-3

Verified Answer :

GinnyAnswer

To solve the given system of linear equations using substitution, let's approach each set of equations step-by-step.

System 1:

1. \(\( y = -2x - 9 \)\)
2. \(\( 6x - 5y = -19 \)\)

Step 1: Substitute \(\( y \)\) from the first equation into the second equation.
\(\[ 6x - 5(-2x - 9) = -19 \]\)

Step 2: Simplify and solve for \(\( x \)\).
\(\[ 6x + 10x + 45 = -19 \]\)
\(\[ 16x + 45 = -19 \]\)
\(\[ 16x = -64 \]\)
\(\[ x = -4 \]\)

Step 3: Substitute \(\( x = -4 \)\) back into the first equation to find \(\( y \)\).
\(\[ y = -2(-4) - 9 \]\)
\(\[ y = 8 - 9 \]\)
\(\[ y = -1 \]\)

So, the solution to the first system is \(\( (x, y) = (-4, -1) \)\).

System 2:

1. \(\( x = 6y - 7 \)\)
2. \(\( 4x + y = -3 \)\)

Step 1: Substitute \(\( x \)\) from the first equation into the second equation.
\(\[ 4(6y - 7) + y = -3 \]\)

Step 2: Simplify and solve for \(\( y \)\).
\(\[ 24y - 28 + y = -3 \]\)
\(\[ 25y - 28 = -3 \]\)
\(\[ 25y = 25 \]\)
\(\[ y = 1 \]\)

Step 3: Substitute \(\( y = 1 \)\) back into the first equation to find \(\( x \)\).
\(\[ x = 6(1) - 7 \]\)
\(\[ x = 6 - 7 \]\)
\(\[ x = -1 \]\)

So, the solution to the second system is \(\( (x, y) = (-1, 1) \)\).

Therefore, the solutions are:
1. \(\( (x, y) = (-4, -1) \)\)
2. \(\( (x, y) = (-1, 1) \)\)