Without solving or graphing, predict the number of solutions to the system. Explain your decision.

Question

y = 3x - 2

3x + y + 2 = 0

Answer 1

one solution

they're linearly independent equations

they're both graphically straight lines, with different slopes. They intersect only once, at the point that's the solution to the system of equations

solve the 2nd for y, and the coefficient of the x term is the slope = -3. slope of the 1st equation is +3

they're graphically 1st going upwards, 2nd downwards

they both have the same y intercept, -2

they intersect at the y-intercept (0,-2)

y=3x -2

y=-3x -2

-2=3(0)-2 = -2

-2=-3(0)-2= -2