solve by substitution   y= -6x+5      -2x+y=5        x=      y=   

To solve the system of equations using substitution, we can follow these steps:

Given equations:
1. \( y = -6x + 5 \) 
2. \( -2x + y = 5 \)

**Step 1: Substitute the expression for \( y \) from the first equation into the second equation.**

Since \( y = -6x + 5 \), we can replace \( y \) in the second equation:

\[
-2x + (-6x + 5) = 5
\]

Simplify the equation:

\[
-2x - 6x + 5 = 5
\]

\[
-8x + 5 = 5
\]

**Step 2: Solve for \( x \).**

Subtract 5 from both sides:

\[
-8x = 0
\]

Divide by \(-8\):

\[
x = 0
\]

**Step 3: Substitute \( x = 0 \) into the first equation to find \( y \).**

\[
y = -6(0) + 5
\]

\[
y = 5
\]

So, the solution is:

\[
x = 0, \quad y = 5
\]

Would you like further details on this solution, or do you have any questions? Here are some related problems you might find interesting:

1. Solve the system using the elimination method: \(3x + 2y = 12\) and \(x - y = 3\).
2. Find the intersection point of the lines represented by the equations \(2x - 3y = 6\) and \(4x + y = 7\).
3. Solve by substitution: \(y = 3x - 4\) and \(5x - y = 11\).
4. Determine if the system \(x + y = 1\) and \(2x + 2y = 2\) has one solution, no solution, or infinitely many solutions.
5. Use substitution to solve the system: \(2y = 4x - 6\) and \(3x - y = 7\).

**Tip:** When solving systems of equations by substitution, always start by isolating one variable in one of the equations to make the substitution easier.

solve by substitution y= -6x+5 -2x+y=5 x= y=

Learn how to solve the system of linear equations y = -6x + 5 and -2x + y = 5 using the substitution method. This step-by-step guide covers essential algebraic concepts for solving systems of equations and is suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation