MathematicsGrade 9en

📐 Solving Systems with Substitution

Master the substitution method for solving systems of linear equations step by step. **What you'll learn:** - Isolate a variable in one equation and substitute into the other - Solve systems of two linear equations using substitution - Check solutions by substituting back into both original equations - Identify when a system has one solution, no solution, or infinitely many solutions - Apply substitution to real-world problems involving two unknowns

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Question 1
What is the first step when using the substitution method to solve a system of equations?
Question 2
In the system $y = 2x + 1$ and $x + y = 7$ , what should you substitute for $y$ in the second equation?
Question 3
If $y = 3x$ and $x + y = 12$ , then substituting gives $x + 3x = 12$ , which simplifies to $4x = 12$ . Therefore, $x = ___$ .
Question 4
Solve the system: $x = 2y$ and $3x + y = 14$ . What is the value of $x$ ?
Question 5
Once you find the value of one variable using substitution, you always need to substitute that value back into one of the original equations to find the other variable.
Question 6
Solve the system: $2x + y = 5$ and $y = x - 1$ . What is the solution $(x, y)$ ?
Question 7
In the system $y = -x + 3$ and $2x + 2y = 6$ , how many solutions does this system have?
Question 8
Solve the system $3x - y = 5$ and $y = 2x - 3$ . The value of $x$ is ___ and the value of $y$ is ___.
Question 9
A shop sells notebooks and pens. Three notebooks and two pens cost 10 dollars. If one notebook costs twice as much as one pen, which system represents this situation? (Let $n$ = cost of a notebook, $p$ = cost of a pen)
Question 10
Using the system $3n + 2p = 10$ and $n = 2p$ from the previous problem, what is the cost of one pen in dollars?