To solve the system of two equations, you need not graph the equations. You can solve one of the equations for either of the variables and then substitute the "value" of that variable into the other equation as shown below.
4x=y+5 (subtract 5 from each side)
4x–5=y (now we know the "value" of y)
8x–5=2y (substitute the above "value" of y into this equation)
8x–5=2(4x–5) (get rid of parentheses by multiplying)
8x–5=8x–10 (solve for x by subtraction 8x from each side of the equal sign)
–5=–10 (not a true statement, so . . .
There is NO solution to this system of equations. The two lines do NOT intersect.
You may graph the equations by picking three values for x (say, -1, 0, and 1), substituting these values, one at a time, into each equation to determine the corresponding values of y for each value of x. You will have three ordered pairs for each equation. Technically, you only need two to find the line, but finding three covers your rear end in case you make a mistake.
Plot each set of three ordered pairs or points. Connect the dots. You have two lines. There are three choices, the lines are identical, the lines intersect in one point, or the lines do not intersect at all.
4x=y+5 (subtract 5 from each side)
4x–5=y (now we know the "value" of y)
8x–5=2y (substitute the above "value" of y into this equation)
8x–5=2(4x–5) (get rid of parentheses by multiplying)
8x–5=8x–10 (solve for x by subtraction 8x from each side of the equal sign)
–5=–10 (not a true statement, so . . .
There is NO solution to this system of equations. The two lines do NOT intersect.
You may graph the equations by picking three values for x (say, -1, 0, and 1), substituting these values, one at a time, into each equation to determine the corresponding values of y for each value of x. You will have three ordered pairs for each equation. Technically, you only need two to find the line, but finding three covers your rear end in case you make a mistake.
Plot each set of three ordered pairs or points. Connect the dots. You have two lines. There are three choices, the lines are identical, the lines intersect in one point, or the lines do not intersect at all.
