To eliminate the variable x when the two equations are added together, multiply the first equation by 8.
To eliminate the variable x when the two equations are added together, we need to multiply the first equation by a constant factor. Let's manipulate the equations:
First, let's multiply the first equation by 8 to eliminate the x variable:
16x + 8y = 80
Next, we'll add this modified equation to the second equation:
16x + 4y + 16x + 8y = 8 + 80
Combine like terms:
32x + 12y = 88
So, by multiplying the first equation by 8, we effectively eliminated the variable x when the two equations were added together.
The probable question may be:
In a network optimization scenario, two equations represent the traffic flow and bandwidth constraints for different routes. The equations are:
2x−3y=10
16x+4y=8
To enhance network efficiency, what constant factor should be multiplied by the first equation (top equation) to eliminate the variable x when the two equations are added together? Consider this as a data communication problem where x represents the data packets transmitted, and y represents the bandwidth capacity. How can we manipulate the equations to ensure optimal data flow within the network?
Additional Information:
Assume x represents the number of data packets transmitted in a network, y represents the available bandwidth, and the constants in the equations correspond to specific network parameters. Optimal network performance is achieved when the two equations are combined effectively, and the variable x is eliminated.