solve the system of eqations 5x−4y=−10 if y=2x-5

Answer 1

It's not an if; it's an and. You are looking for the point that solves both equations (also where they cross when graphed).

These really used to confuse me, but we are going to substitute. Since we have a "value" for y, we can substitute it for y in the 1st equation.

5x - 4(2x - 5) = -10

5x - 8x + 20 = -10

-3x = -30

x = 10

Now, we substitute 10 for x in either equation.

y = 2(10) - 5

y = 20 - 5

y = 15

(10,15)

Answer 2

To solve" means to find the point (x,y) that satisfies these two equations. Since they are both equations of lines, point (x,y) is intersection of the two lines. There may be (a) one point for (x,y), (b) no point for (x,y) -- the lines are parallel and don't ever intersect, or (c) an infinite number of solution -- if the two equations represent the same line.

In addition to solving the system graphically, you may solve it algebraically by (1) substitution or by (2) elimination.

With each method you first find wither x or y, then you use that value to find the other one..

The system of equations:

5x −4y = −10

y = 2x - 5

is ready-made to solve for y in terms of x (already done) and then solve for x.

(1) substitution:

Replace y in the first equation with the value of y in terms of x. That leaves only x.

5x -4(2x-5) = -10

5x - 8x + 20 = -10 [expand]

-3x = -30 [combine terms and subtract 20 from each side]

x = 10 [divide both sides by (-3)]

Use either equation to get the value of y. The second equation looks easiest:

y = 2x - 5

y = 2(10) - 5

y = 15

It is always good to check:

Is 5(10) - 4(15) = -10 ?

50 - 60 = -10 ?

-10 = -10 ?yes

Is 2(10) - 5 = 15 ?

20 - 5 = 15 ?

15 = 15 ?yes

(2) Elimination

Add or subtract equations to eliminate one variable. You might have to get both variables on the same side of the equation.

5x - 4y = -10

-2x + y = -5

and .. we might have to multiply one equation or both by constants to get a common coefficient:

5x - 4y = -10

-8x + 4y = -20 [second equation times 4]

---------------------------- [elimination; add equations]

-3x + 0 = -30

x = 10

How, you may either substitute 10 for x or form another elimination to find the value for y.

If you have not performed a check, be sure to do one !