To solute or not solute

Determine if coordinate (1,4) is a solution for the systems below

y=x+3            y=2x-2

4=1+3            4=2(1)-2

4=4                 4=0

CHECK           DOES NOT CHECK

The solution is not a solution for this system of equations

y=5x -1        y=-2x + 6

4=5(1)-1      4= -2(1)+6

4=4                4=4

CHECK          CHECK

The solution is a solution for this system of equations

Problem:

y=5x-1
y=-2x+6

GRAPHING SYSTEMS OF EQUATIONS

y=-3x+2
y=3x-4

solution (1, -1)

There are two ways to graph a system of equations. If the equations are presented

in y-intercept form, then you would plot your first point at the y-intercept. Then,

you would use the slope (mx) to plot your remaining points. The solution will always be the location in which the two lines intersect.

Secondly, you can use the substitution method to find your x and y value for each equation. To prove that your solution is correct, graph each of the lines by placing them in y-intercept form. If the solution that you receive after you create your graph is the same as the solution you developed with using the substitution method, then your answer is correct.

ex.     x + y = 4

2x  – y = 5

Step 1: put the first equation into y-intercept form (y = -x + 4)

Step 2: substitute the new equation into the second-given equation (2x – (-x + 4) = 5)

Step 3: combine like terms (2x + x + 4 =5) –> (3x + 4 = 5) —> (3x – 4+4 = 5+4) —>

(3x/3 = 9/3) —>x = 3

Step 4: substitute the new equation into the first-given equation (3+ y = 4)

Step 5: subtract 1/3 from both sides of the equation (3-3 + y = 4 -3)

Step 6: solve (y = 4 – 3) —> y = 1

Step 7: write your solution ( 3, 1)

Step 8: make a graph to check your solution ( 3+1=4 ), ( 2(3) – 1 = 5) CHECK!