Grade 9 · Algebra & functions

Systems of equations practice

Systems of equations is a grade 9 math skill aligned to Common Core standard HSA.REI.C.6: solve systems of linear equations exactly and approximately, focusing on pairs of linear equations in two variables. Below are 8 practice questions with answers and step-by-step explanations, drawn from the 20 systems of equations problems our math games drill.

CCSS HSA.REI.C.620 questions in the bank

Sample questions

Try 8 for free

Question 1easy

Solve the system: $\begin{cases} x + y = 5 \ x - y = -1 \end{cases}$
What is the value of $x$ ?

Add the equations: $2x = 4$ , so $x = 2$ .

Question 2easy

If $y = x + 3$ and $x + y = 9$ , what is the value of $x$ ?

Substitute: $x + (x + 3) = 9$ , so $2x = 6$ and $x = 3$ .

Question 3easy

Solve the system: $\begin{cases} x + y = 3 \ x - y = -5 \end{cases}$
What is the value of $x$ ?

Add the equations: $2x = -2$ , so $x = -1$ .

Question 4easy

Two lines satisfy $y = 3x$ and $y = x + 10$ . What is the $x$ -value of the solution?

Set the expressions equal: $3x = x + 10$ , so $2x = 10$ and $x = 5$ .

Question 5easy

Solve the system: $\begin{cases} x + y = 3 \ x - y = 7 \end{cases}$
What is the value of $x$ ?

Add the equations: $2x = 10$ , so $x = 5$ .

Question 6easy

Solve the system: $\begin{cases} x + y = 4 \ x - y = 2 \end{cases}$
What is the value of $x$ ?

Add the equations: $2x = 6$ , so $x = 3$ .

Question 7easy

Solve the system: $\begin{cases} x + y = 7 \ x - y = -7 \end{cases}$
What is the value of $x$ ?

Add the equations: $2x = 0$ , so $x = 0$ .

Question 8easy

Solve the system: $\begin{cases} x + y = -5 \ x - y = -3 \end{cases}$
What is the value of $x$ ?

Add the equations: $2x = -8$ , so $x = -4$ .

Tests that cover systems of equations:

PSAT 8/9 SAT NAEP NY State Math MCAP

More Grade 9 skills:

Slope-point line equations Slope-intercept intercepts Rational exponents Rational equation solving (SAT)Radical to exponent conversions Quadratic minimum x-value Quadratic formula Quadratic distinct real solutions count All Grade 9 practice →

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