Systems of equations must have 2 or more equations.
graphing – graph the 2 lines.
if the lines are parallel , the slopes are the same and the y-intercepts are different. there are no solutions.
if the lines are the same line, the slopes are the same and the y-intercepts are same . there have infinite solutions.
if the lines are intersecting, the slopes are and the y intercepts can be the . there is one solution, this is where the lines intersect.

he equations in this example are already set equal to "y". identify the slope and y-intercept in each equation. remember: y = mx + b, where m = slope and b = y-intercept.

y = 2x + 1

slope = 2

y-intercept = 1

y = -x + 7

slope = -1

y-intercept = 7

2. graph the lines.

this example used the slope-intercept method of graphing straight lines.

the b-value tells you where the line crosses the y-axis.

the slope, m, tells you the rise over the run.

if you need graphing lines, see graphing linear equations.

find the intersection point (where the lines cross).

these lines cross at the point (2,5).

this means the solution to this system is:

solution: x = 2 and y = 5.

graph1

3. check: substitute x = 2 and y = 5 into both of the original equations. if your solutions are correct, both equations will be true!

y = 2x + 1

5 = 2(2) + 1

5 = 5 (check)

y = -x + 7  

5 = -(2) + 7

5 = 5 (check)

step-by-step explanation:

- 2 + 10x³ - 21x² + 19x - 4

step-by-step explanation:

each term in the second factor is multiplied by each term in the first factor

x²(- 2x² + 4x - 1) - 3x(- 2x² + 4x - 1) + 4(- 2x² + 4x - 1) ← distribute

= - 2 + 4x³ - x² + 6x³ - 12x² + 3x -8x² + 16x - 4

collect like terms

= - 2 + 10x³ - 21x² + 19x - 4 ← in standard form

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step-by-step explanation:

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