Task Sets: Solve real-world and mathematical problems leading to two linear equations in two variables - Common Core Math - Grade 8

Recall / Warm-Up

Line $p$ has slope $2$ and line $q$ has slope $-3$ . Based on their slopes alone, what can you conclude about these two lines?

They intersect at exactly one point.

They are parallel and never intersect.

They are the same line.

Not enough information to tell.

Is the pair $x = 4$ , $y = 1$ a solution of the system $x + y = 5$ and $2x - y = 7$ ?

Yes — it satisfies both equations.

No — it satisfies only the first equation.

No — it satisfies only the second equation.

No — it satisfies neither equation.

A bag holds $x$ red marbles and $y$ blue marbles. There are $30$ marbles in all. Write the equation for the total number of marbles. Enter the number that the expression $x + y$ equals.

Fluency Practice

A concert sold $a$ adult tickets and $s$ student tickets. There were $90$ tickets sold in all, and adult tickets cost $\text{\char"0024}12$ while student tickets cost $\text{\char"0024}7$ , for total sales of $\text{\char"0024}880$ . Which system represents this situation?

$a + s = 90$ and $12a + 7s = 880$

$a + s = 880$ and $12a + 7s = 90$

$12a + 7s = 90$ and $a + s = 880$

$a + s = 90$ and $19(a + s) = 880$

Solve the system by substitution: $y = x + 3$ and $2x + y = 18$ . Enter the value of $x$ .

Solve the system by elimination: $x + y = 14$ and $x - y = 2$ . Enter the value of $y$ .

Solve the system: $3x + 2y = 16$ and $x = 2y$ . Enter the value of $x$ .

Line $1$ passes through $(0, 1)$ and $(2, 5)$ . Line $2$ passes through $(1, 0)$ and $(3, 4)$ . Do these two lines intersect?

No — both lines have slope $2$ but different $y$ -intercepts, so they are parallel.

Yes — they intersect at exactly one point.

Yes — they are the same line, so they meet everywhere.

No — the lines have different slopes, so they cannot meet.

Exercises: Solving Real-World and Mathematical Problems with Systems of Linear Equations

Recall / Warm-Up

Fluency Practice