Question

Given the system of linear equations.

x + y = 7
2x + y = 5

Part A: Solve the system of linear equations using substitution
Part B: Use a graph to verify your answer to the system
In your final answer, include all of your work for both Parts A and B as well as the graph for Part B.

Answer 1

the answer is negative two

Explanation:

Answer 2

Part(A):

To solve the system of Linear equations using Substitution:

`x+y=7 \\ 2x+y=5`

Consider the first equation, x+y=7 implies x=7-y

`\mathrm{Subsititute\:}x=7-y`

`2\left(7-y\right)+y=5`

`14-2y+y=5`

`14-y=5`

`\mathrm{Subtract\:}14\mathrm{\:from\:both\:sides}`

`14-y-14=5-14`

`-y=-9`

`\mathrm{Divide\:both\:sides\:by\:}-1`

`y=9`

`\mathrm{For\:}x=7-y`

`\mathrm{Subsititute\:}y=9`

`x=7-9=-2.`
`\mathrm{The\:solutions\:to\:the\:system\:of\:equationts\:are:}`

`y=9,\:x=-2`

PArt(B): Use a graph to verify your answer to the system:

Using Desmos graphing calculator, graph the two equations.