WHERE IS the point R

The line y=2x-3 meets the x-axis at the point P, and the line 3y+4x=8 meets the x-axis at the point Q. The two lines intersect at the point R.

find the coordinates of R

i really dont know how to do this

please show me how to do it

thank you

You need to solve the two equations together

One way to do this is to use the first equation in the second:

y=2x-3
3y+4x=8

so

3(2x-3) + 4x = 8

You now need to expand the brackets and do some algebra to find the x co-ordinate of R, the use the first equation to find y.

You should get x=1.7 and y=0.4

Another way would be to draw graphs for both lines.

Y = 2X -3 and 3Y + 4X = 8 are two lines which intersect at point R.
Let's rewrite the two equations as Y = something

Y = 2X - 3 ..................first line equation unchanged (equation 1)
Y = ( 8 - 4X)/3 ...........subtracted 4X from both sides and divided both sides by 3 (equation 2)

If the lines intersect this means that at the point of intersection both lines are equal i.e. the point of intersection lies on both lines. This means that:

2X - 3 = (8 - 4X)/3 ......make the two lines equal

6X - 9 = 8 - 4X ...........multiply both sides of the equation above by 3
10X = 17 ............put the Xs on one side and the constants on the other
X = 17/10
We now find Y
from the equation of the first line we have:

Y = 2*17/10 - 3 = (34 -30)/10 = 4/10 = 2/5
from equation 2

Y = (8 - 4*17/10)/3 = (8 - 2*17/5)/3 = (40 - 34)/15 = 6/15 = 2/5

so the point of intersection is (17/10, 2/5)

y = 2x - 3
y = (-4x+8)/3

the lines intercepts when y1=y2 and x1=x2

2x - 3 = -4/3 x + 8/3

2x + 4/3 x = 3 + 8/3

6x + 4x = 9 + 8
10x = 17
x= 17/10

x= 1.7
y= 2(1.7)-3
y= 0.4