Using the graphing method what is the point of intersection for this system?!


Question: 5x - y = 4
4x + 2y = 6

please help and try to explain, obviously if i could graph them myself i would have done it already i just keep second guessing myself.


Answers: 5x - y = 4
4x + 2y = 6

please help and try to explain, obviously if i could graph them myself i would have done it already i just keep second guessing myself.

first you have to solve for y for each equation.
subtract 5x from both sides.
then you would have -y = 4 - 5x
now switch the signs to get a positive y value.
y = -4 + 5x
do the same for the second equation, but divide by 2 as well.
4x + 2y = 6
2y = 6 - 4x
divide by 2 to get y by itself.
y = 3 - 2x
afterwards, you can graph them to find the intersection. its pretty simple with a graphing calculator, but here's how you do it by hand.
the number without a variable (x or y) is the y-intercept. on the graph paper, this means when the equation crosses the y axis and x = 0. the vertical line (up and down) is the y axis. the horizontal (left to right) line is the x axis.
graph one equation at a time. to graph y = -4 +5x first draw a point at (0, -4). this means a point at -4 on the y axis. the slope is 5x. this is equal to rise/run. because it is five, go up five and over one. this is where your next point will be. (1, 1)
keep following this pattern until you have a long enough line.
then graph the second equation the same way.
y = 3 - 2x
first graph the y intercept at 3. so (0, 3) would be your first point. the slope is -2. so that means you would go up 2 and over one, but to the LEFT because it is negative. so (-1, 5) would be your next point. again, follow the same pattern to get a long enough line.
once you graph both equations, they should intercept. just look up the coordinates on the graph you drew and there you go. hope this explains it well enough, i haven't taken a math class in years.



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