Grade 9 · Algebra & functions

Linear systems by substitution (SAT) practice

Linear systems by substitution (SAT) 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 10 linear systems by substitution (sat) problems our math games drill.

CCSS HSA.REI.C.610 questions in the bank
Sample questions

Try 8 for free

Question 1easy

{y=x+8 4x+y=14\begin{cases} y = -x + 8 \ 4x + y = 14 \end{cases}
The solution to this system is
(x,y)(x, y). What is the value of x+yx + y?

Substitute y=x+8y = -x + 8 into the second equation: 4xx+8=144x - x + 8 = 14, so 3x=63x = 6 and x=2x = 2. Then y=6y = 6, and x+y=8x + y = 8.

Question 2easy

At a cafe, a cup of coffee costs $c\text{\char36}c and a cup of tea costs $t\text{\char36}t. A cup of coffee costs $2\text{\char36}2 more than a cup of tea. One cup of tea and two cups of coffee cost $16\text{\char36}16 in total. What is the price of one cup of coffee?

The system is c=t+2c = t + 2 and t+2c=16t + 2c = 16. Substitute: t+2(t+2)=16t + 2(t + 2) = 16, so 3t+4=163t + 4 = 16, t=4t = 4, and c=6c = 6.

Question 3easy

A rental shop charges $b\text{\char36}b per hour to rent a bike and $s\text{\char36}s per hour to rent a scooter. The scooter rental costs $3\text{\char36}3 more per hour than the bike rental. Renting one bike for 22 hours and one scooter for 11 hour costs $18\text{\char36}18 in total. What is the hourly rate to rent a bike?

The system is s=b+3s = b + 3 and 2b+s=182b + s = 18. Substitute: 2b+(b+3)=182b + (b + 3) = 18, so 3b=153b = 15 and b=5b = 5.

Question 4easy

A museum sells student tickets for $s\text{\char36}s each and adult tickets for $a\text{\char36}a each. An adult ticket costs $7\text{\char36}7 more than a student ticket. One adult ticket and two student tickets cost $28\text{\char36}28 in total. What is the price of one student ticket?

The system is a=s+7a = s + 7 and a+2s=28a + 2s = 28. Substitute: (s+7)+2s=28(s + 7) + 2s = 28, so 3s=213s = 21 and s=7s = 7.

Question 5easy

A parking garage charges $h\text{\char36}h for one hour of parking and $d\text{\char36}d for a daily pass. A daily pass costs 44 times as much as one hour of parking. Buying one hour of parking and one daily pass costs $15\text{\char36}15 in total. What is the price of a daily pass?

The system is d=4hd = 4h and h+d=15h + d = 15. Substitute: h+4h=15h + 4h = 15, so 5h=155h = 15, h=3h = 3, and d=12d = 12.

Question 6medium

{y=2x+3 3x+2y=27\begin{cases} y = 2x + 3 \ 3x + 2y = 27 \end{cases}
The solution to this system is
(x,y)(x, y). What is the value of yy?

Substitute y=2x+3y = 2x + 3 into the second equation: 3x+2(2x+3)=273x + 2(2x + 3) = 27, so 3x+4x+6=273x + 4x + 6 = 27, 7x=217x = 21, x=3x = 3, and y=9y = 9.

Question 7medium

{p=q+5 3p+2q=40\begin{cases} p = q + 5 \ 3p + 2q = 40 \end{cases}
The solution to this system is
(p,q)(p, q). What is the value of qq?

Substitute p=q+5p = q + 5 into the second equation: 3(q+5)+2q=403(q + 5) + 2q = 40, so 3q+15+2q=403q + 15 + 2q = 40, 5q=255q = 25, and q=5q = 5.

Question 8medium

At a snack bar, a bag of chips costs $c\text{\char36}c and a candy bar costs $d\text{\char36}d. A candy bar costs twice as much as a bag of chips. Buying 33 bags of chips and 22 candy bars costs $21\text{\char36}21 in total. What is the price of one candy bar?

The system is d=2cd = 2c and 3c+2d=213c + 2d = 21. Substitute: 3c+2(2c)=213c + 2(2c) = 21, so 7c=217c = 21, c=3c = 3, and d=6d = 6.

Drill it inside a game.

The free placement test finds your level, then every match serves linear systems by substitution (sat) questions at exactly the right difficulty.