Question

Find an equivalent system of equations for the following system:

2x + 4y = 4
-5x + 5y = 5

A.2x + 4y = 4
-3x - y = -1

B.2x + 4y = 4
7x + 5y = -1

C.2x + 4y = 4
7x - y = 5

D.2x + 4y = 4
7x - y = -1​

Answer 1

`\large\boxed{D.\ \left\{\begin{array}{ccc}2x+4y=4\\7x-y=-1\end{array}\right}`

Step-by-step explanation:

`\left\{\begin{array}{ccc}2x+4y=4\\-5x+5y=5&\text{change the signs}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}2x+4y=4&(1)\\5x-5y=-5\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad7x-y=-1\qquad(2)\\\\\text{The equivalent system of equations: use (1) and (2)}\\\\\left\{\begin{array}{ccc}2x+4y=4\\7x-y=-1\end{array}\right`

Answer 2

A.2x + 4y = 4

-3x - y = -1

D.2x + 4y = 4

7x - y = -1​

Step-by-step explanation:

Given system of equations,

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

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

x-intercept and y-intercepts of equation (1) are (2, 0) and (0, 1)

While, x-intercepts and y-intercepts of equation (2) are (-1, 0) and (0, 1)

Thus, by plotting these lines on the graph,

We get,

The intersection point of line (1) and (2) is ( 0, 1)

That is, the solution would be (0, 1),

Similarly,

Graphing -3x - y = -1, 7x + 5y = -1, 7x - y = 5 and 7x - y = -1,

We get,

A. The solution of 2x + 4y = 4, -3x - y = -1 is ( 0, 1 )

B. The solution of 2x + 4y = 4, 7x + 5y = -1 is ( -1.333, -1.667 )

C. The solution of 2x + 4y = 4, 7x - y = 5 is ( 0.8, 0.6)

D. The solution of 2x + 4y = 4, -7x - y = -1​ is ( 0, 1 )