ACT · Mathematics

Systems of linear equations

26 practice questions, each with the answer and an explanation.

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Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 26 questions

If $x + y = 14$ and $x - y = 10$ , what is the value of $y$ ?
If $x + y = 14$ and $x - y = 6$ , what is the value of $y$ ?
If $x + y = 13$ and $x - y = 7$ , what is the value of $y$ ?
If $x + y = 10$ and $x - y = 6$ , what is the value of $x$ ?
If $x + y = 11$ and $x - y = - 1$ , what is the value of $x y$ ?
If $x + y = 15$ and $x - y = 3$ , what is the value of $y$ ?
If $x + y = 9$ and $x - y = - 3$ , what is the value of $y$ ?
If $x + y = 9$ and $x - y = 5$ , what is the value of $x y$ ?
If $x + y = 9$ and $x - y = - 7$ , what is the value of $x$ ?
If $x + y = 6$ and $x - y = - 2$ , what is the value of $x y$ ?
If $x + y = 6$ and $x - y = 4$ , what is the value of $x$ ?
If $x + y = 12$ and $x - y = 2$ , what is the value of $x$ ?
If $x + y = 15$ and $x - y = - 1$ , what is the value of $x$ ?
If $x + y = 13$ and $x - y = - 3$ , what is the value of $x y$ ?
If $x + y = 13$ and $x - y = - 9$ , what is the value of $x y$ ?
If $x + y = 10$ and $x - y = - 4$ , what is the value of $x$ ?
If $x + y = 15$ and $x - y = - 9$ , what is the value of $x y$ ?
If $x + y = 3$ and $x - y = - 1$ , what is the value of $y$ ?
If $x + y = 15$ and $x - y = - 7$ , what is the value of $x y$ ?
If $x + y = 14$ and $x - y = - 4$ , what is the value of $x y$ ?
If $x + y = 13$ and $x - y = - 5$ , what is the value of $x y$ ?
The system $3 x + k y = 9$ and $6 x + 8 y = m$ has infinitely many solutions. What is the value of $k + m$ ?
A boat travels $24$ miles upstream in $4$ hours and then returns the $24$ miles downstream in $2$ hours. If the boat's speed in still water and the current are both constant, what is the boat's speed…
If $\frac{2}{x} + \frac{3}{y} = 7$ and $\frac{4}{x} - \frac{1}{y} = 7$ , what is the value of $x + y$ ?
If $\frac{x}{2} + \frac{y}{3} = 7$ and $\frac{x}{4} - \frac{y}{6} = 0$ , what is the value of $x + y$ ?
For which value of $k$ does the system $k x + 3 y = 6$ and $4 x + (k + 1) y = 8$ have infinitely many solutions?

Systems of linear equations

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