6x + 7y + 35

6x - 3y = -15

To solve the sustem, we will use the elemination method to solve:

Sbtract (2) from (1):

==> 10y = 50

Now divide by 10:

**==> y= 5**

To find x, we will substitute in (2)

6x - 3y = -15

6x = 3y + 15

6x = 15+15= 30

==> x= 30/6

**==> x= 5**

**Then the point where both lines intercept is (5, 5)**

We'll have to put the given equations in the standard form:

y = mx + n, where m is the slope and n is y intercept.

To put it into the standard form, we'll have to isolate y to the left side. For this reason, we'll subtract 6x and add 35 both sides:

7y = -6x + 35

We'll divide by 7 both sides:

y = -6x/7 + 35/7

**y = -6x/7 + 5**

**We notice that the y intercept of the line is 5.**

6x-3y+15=0

To put it into the standard form, we'll have to isolate y to the left side. For this reason, we'll subtract 6x and 15 both sides:

-3y = -6x - 15

We'll divide by 3 both sides:

**y = 2x + 5**

**We notice that the given line has the y intercept of 5, also.**

Let's find both the x and y intercepts of the lines 6x + 7y = 35 and 6x - 3y = -15

Now to find the x intercepts , we need to find the point where the lines intersect the x- axis or where y =0

Therefore

for 6x + 7y = 35

we get 6x + 0 =35 => x= 35/6

and for 6x - 3y = -15

we get 6x = -15 => x = -15/6 = -5/2

Now to find the y intercepts , we need to find the point where the lines intersect the y- axis or where x =0

Therefore

for 6x + 7y = 35

we get 7y + 0 =35 => y= 5

and for 6x - 3y = -15

we get -3y = -15 => y = 5

**Therefore for line:**

**6x + 7y = 35 , x-intercept is 35/6 and y-intercept is 5**

**6x - 3y = -15 , x-intercept is -5/2 and y-intercept is 5**