SAT · ACT · MCATGoal-based prepLive 1:1 + GoalGap AI
ACT · Math · Preparing for Higher Math: Algebra
Linear equations in two variables is part of Preparing for Higher Math: Algebra in the ACT Math section. The questions below are written in the style of the real test, each with the answer and a worked explanation.
Question types you will see here include points on a two-variable line, two-variable model from a context, interpret a coefficient or constant and convert between forms.
Common traps: swapping x and y; substituting into only one term; a sign error with a negative.
Question 1
The point (3, −2) lies on the line 4x + ky = 20. What is the value of k?
−4
4
8
28/3
Answer: A. −4
4(3) + k(−2) = 20 gives 12 − 2k = 20, so −2k = 8 and k = −4. 4 loses the sign when dividing by −2; 8 stops at −2k = 8; 28/3 substitutes the coordinates in the wrong order: 4(−2) + 3k = 20.
Question 2
At a cricket academy shop in Chennai, a bat grip costs ₹150 and a ball costs ₹400. Ananya spends exactly ₹2,300 on g grips and b balls. Which equation models this purchase?
400g + 150b = 2,300
150g + 400b = 2,300
g + b = 2,300
550(g + b) = 2,300
Answer: B. 150g + 400b = 2,300
Each grip adds ₹150 and each ball adds ₹400, so the costs are 150g and 400b and their sum is 2,300. A attaches the prices to the wrong items; C adds the counts as if they were costs; D charges ₹550 for every item.
Question 3
A taxi in Mumbai charges a fixed ₹50 plus ₹22 per kilometre. Which equation gives the fare F, in rupees, for a ride of d kilometres?
F = 50 + 22d
F = 22 + 50d
F = 72d
F ≥ 50 + 22d
Answer: A. F = 50 + 22d
The fixed charge is added once and ₹22 is charged for each kilometre, so F = 50 + 22d. B swaps the fixed charge and the rate; C charges ₹72 per kilometre with no fixed part; D uses an inequality where an exact fare is described.
Question 4
What are the slope and y-intercept of the line −6x + 3y = −12 in the standard (x, y) coordinate plane?
Slope −2, y-intercept 4
Slope −6, y-intercept −12
Slope 2, y-intercept −4
Slope 2, y-intercept −12
Answer: C. Slope 2, y-intercept −4
3y = 6x − 12, so y = 2x − 4: slope 2 and y-intercept −4. A flips both signs when moving −6x; B reads the standard-form coefficients directly; D divides the x-term by 3 but not the constant.
Question 5
In the standard (x, y) coordinate plane, what is the y-intercept of the line 3x − 5y = 20?
−4
4
20/3
20
Answer: A. −4
Set x = 0: −5y = 20, so y = −4. 4 drops the sign when dividing by −5; 20/3 is the x-intercept (set y = 0 instead); 20 reads the constant in standard form as the intercept.
A few questions show the style. The free scan shows which ACT skills cost you the most points, then builds a plan around them.