Algebra 1 Unit 4: Systems of Equations and Inequalities

Solving systems by substitution, elimination and graphing, counting solutions, and systems from word problems. 12 questions. Have a go at each one on paper before you tap "Show me how".

A free account opens the worked solutions to 20 questions a day; Pro opens every one.

Question 1

SubstitutionNo calculator

Solve the system: $y=2x-1$ and $3x+y=14$.

1. $(3,5)$
2. $(2,3)$
3. $(3,-5)$
4. $(5,3)$

Question 2

EliminationNo calculator

Solve the system: $2x+3y=7$ and $4x-3y=-1$.

1. $(1,3)$
2. $\left(\frac{5}{3},1\right)$
3. $(-1,3)$
4. $\left(1,\frac{5}{3}\right)$

Question 3

Number of solutionsNo calculator

How many solutions does the system $y=3x+2$ and $6x-2y=8$ have?

1. Infinitely many
2. No solution
3. Exactly one
4. Exactly two

Question 4

Systems from contextNo calculator

A school sold 120 tickets to a play. Adult tickets cost 9 dollars and student tickets cost 5 dollars, and the school took in 820 dollars. How many adult tickets were sold?

1. $65$
2. $60$
3. $45$
4. $55$

Question 5

Systems from contextNo calculator

A jar holds only nickels and quarters: 32 coins worth 4.40 dollars in all. How many quarters are in the jar?

1. $16$
2. $14$
3. $18$
4. $12$

Question 6

Number of solutionsNo calculator

For what value of $k$ do $kx+6y=18$ and $2x+3y=9$ have infinitely many solutions?

1. $-4$
2. $6$
3. $4$
4. $2$

Question 7

Systems of inequalitiesNo calculator

Which point is a solution of the system $y>2x-3$ and $y\le -x+4$?

1. $(-2,7)$
2. $(3,4)$
3. $(0,-4)$
4. $(1,2)$

Question 8

SubstitutionNo calculator

Use substitution to find the point where $x=2y+1$ and $3x-4y=11$ are both true.

1. $(-7,-4)$
2. $(9,4)$
3. $(5,2)$
4. $(4,9)$

Question 9

EliminationNo calculator

Two numbers $x$ and $y$ satisfy both $3x+2y=17$ and $2x+3y=13$. Without finding $x$ and $y$ one at a time, work out their sum.

1. $6$
2. $4$
3. $30$
4. $7$

Question 10

Systems from contextNo calculator

A chemist mixes a 10% acid solution with a 30% acid solution to make 40 liters of a 25% acid solution. How many liters of the 10% solution does she use?

1. $30$
2. $15$
3. $10$
4. $20$

Question 11

Graphing systemsNo calculator

At what point do the lines $y=-x+6$ and $y=\frac{1}{2}x-3$ intersect?

1. $(0,6)$
2. $(2,4)$
3. $(-6,12)$
4. $(6,0)$

Question 12

Systems of inequalitiesNo calculator

A club sells cookies for 2 dollars and brownies for 3 dollars. It needs at least 300 dollars and can bake at most 120 items. Which pair (cookies, brownies) meets both conditions?

1. $(60,50)$
2. $(50,70)$
3. $(40,90)$
4. $(90,30)$