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Quantitative Reasoning

Linear equations, graphs, and systems — ISEE Upper practice questions

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Practice 90 Linear equations, graphs, and systems questions in the app

What this topic is

Slope is rise over run, and in Linear equations, graphs, and systems it is often the first quantity to find.

Between two points, subtract the y-values and divide by the difference of the x-values in the same order; mixing the order flips the sign, and a sign-flipped value is usually among the choices. Intercepts come from setting one variable to zero: for the line two x plus y equals six, the x-intercept is three and the y-intercept is six.

Systems of two equations are often solved fastest by adding them so one variable cancels. Word problems typically describe two totals and ask for one of the quantities.

Sample questions

Pick an answer to see whether it is right — nothing is saved, and nothing needs an account.

Question 1Mid

At a bake sale, the number of cookies sold, $c$ , and the number of brownies sold, $b$ , are related by the equations $c + b = 20$ and $2 c - b = 13$ . If $c$ and $b$ are both positive integers, how many brownies were sold?

7✗ Not this one8✗ Not this one9✓ Correct11✗ Not this one

Show answer

Answer: C — 9

Adding the two equations eliminates $b$ : $3 c = 33$ , so $c = 11$ . Substituting into $c + b = 20$ gives $b = 9$ .

Question 2Easier

A line passes through the points $(0, 4)$ and $(6, 1)$ . What is the slope of the line?

- \frac{1}{3}

✗ Not this one

\frac{1}{2}

✗ Not this one

- \frac{1}{2}

✓ Correct

\frac{3}{2}

✗ Not this one

Show answer

Answer: C — $- \frac{1}{2}$

Slope $= \frac{1 - 4}{6 - 0} = \frac{- 3}{6} = - \frac{1}{2}$ .

Question 3Easier

What are the intercepts of the line $6 x - 5 y = 30$ ?

(5, 0)

and

(0, - 6)

✓ Correct

(- 5, 0)

and

(0, 6)

✗ Not this one

(6, 0)

and

(0, - 5)

✗ Not this one

(5, 0)

and

(0, 6)

✗ Not this one

Show answer

Answer: A — $(5, 0)$ and $(0, - 6)$

Setting $y = 0$ gives $x = 5$ , and setting $x = 0$ gives $y = - 6$ . Thus, the intercepts are $(5, 0)$ and $(0, - 6)$ .

Every question is picked for where you are right now, wrong answers come back until they stick, and it all works offline.

Practice 90 Linear equations, graphs, and systems questions in the app

Linear equations, graphs, and systems — ISEE Upper practice questions

What this topic is

Sample questions

More ISEE Upper topics

Quantitative Reasoning