System of Linear Equations

System of Linear Equations Warmup

How many solutions are there for this system of equations? $\begin{aligned} x + y = 4\\ x + y = 6 \end{aligned}$

0 1 Infinity

by Brilliant Staff

Lines $a, b,$ and $c$ represent three different linear equations. What is the solution for the system of $a$ and $c?$

(3,-3) (-3,3) (1,5) (5,1)

by Brilliant Staff

Two of these lines intersect at a point with positive coordinates. Which two?

A: $y = -3x -2$

B: $y = 3x -2$

C: $y = 0.5x +1$

D: $x = -3$

A and B A and C B and C B and D

by Brilliant Staff

Find $xy$ if $2x + 4y = 2$ and $y - x = 5$ .

-6 5 6 -5

by Brilliant Staff

How many $(x, y)$ pairs are solutions for both of these equations?

$\begin{aligned} x + 2y &= 4 \\ 3x + 6y &= 12 \end{aligned}$

0 1 2 infinitely many

by Brilliant Staff