Question

A system of equations is given below.
2x + 7y = 1
-3x – 4y = 5
a. Create an equivalent system of equations by replacing the first equation by multiplying the first equation by an integer other than 1, and adding it to the second equation.

Answer 1

i really need help with this i have been working on it for about 2 hours

Answer 2

This is a poorly phrased question. However, we can follow the instructions and answer it. I choose to multiply the first equation by 3/2, then add it to the second equation. We will take that sum and the first equation to be our new system of equations.

Answer 3

Multiply both sides by 3/2\[2x+7y=1 \implies 3x+\frac{21y}{2}=\frac{3}{2}\]Add the equations together\[3x-3x+\frac{21y}{2}-4y=\frac{3}{2}+5 \implies \frac{13y}{2}=\frac{13}{2} \implies y=1\]So our system of equations is\[2x+7y=1\]\[y=1\]

Answer 4

From the above, the only step left to solve the system is to substitute the second equation (y = 1) into the first equation and solve. If we substitute, we get\[2x+7=1 \implies 2x=-6 \implies x=-3\]So the solution of the system is\[(x,y)=(-3,1)\]