Question

Use the system of equations and graphs below to complete the sentences ​

Answer 1

The correct graph is: Graph C

and the solution for this system is: (2,1)

Explanation:

The first equation is given by:

`x-4y=-2-------(1)`

and the second equation is given by:

`-2x-y=-5----------(2)`

from (1) we have:

`x=-2+4y-------------(3)`

We put the value of x in equation (2) to get:

`-2(-2+4y)-y=-5\\\\i.e.\\\\-2* (-2)-2* 4y-y=-5\\\\i.e.\\\\4-8y-y=-5\\\\i.e.\\\\4-9y=-5\\\\i.e.\\\\-9y=-5-4\\\\i.e.\\\\-9y=-9\\\\i.e.\\\\y=1`

Now on putting this value of y back to equation (3) we get:

`x=-2+4* 1\\\\x=-2+4\\\\x=2`

Hence, the solution to this system of equality is: (2,1)

Answer 2

Graph C; (2, 1)

Explanation:

When equations are in standard form, finding the x- and y-intercepts is relatively easy. For ...

ax +by = c

• x-intercept: c/a
• y-intercept: c/b

Using this idea on the first equation, we find its x-intercept to be -2. There is only one graph showing that has a line going through the point (-2, 0). That is Graph C. Checking the remaining intercepts for the two equations confirms that Graph C is the graph of this system of equations.

The two lines intersect at point (2, 1), so that is the solution to the system.