For a system of linear equations to have infinitely many solutions, the two equations must be equivalent. This means they must have the same slope and y-intercept.

The first equation can be rewritten in slope-intercept form (y = mx + b) as follows:

3y = 6x - 12
y = 2x - 4

The slope (m) is 2 and the y-intercept (b) is -4.

The second equation is already in slope-intercept form:

2y = 4x + b
y = 2x + b/2

For the two equations to be equivalent, the slopes must be equal (which they are, both are 2) and the y-intercepts must also be equal. This means that b/2 must be equal to -4.

Solving for b gives:

b/2 = -4
b = -4 * 2
b = -8

So, the value of b that would make the system of equations have infinitely many solutions is b = -8. Therefore, the correct answer is "b is equal to negative 8".

Question

For a system of linear equations to have infinitely many solutions, the two equations must be equivalent. This means they must have the same slope and y-intercept.

The first equation can be rewritten in slope-intercept form (y = mx + b) as follows:

3y = 6x - 12
y = 2x - 4

The slope (m) is 2 and the y-intercept (b) is -4.

The second equation is already in slope-intercept form:

2y = 4x + b
y = 2x + b/2

For the two equations to be equivalent, the slopes must be equal (which they are, both are 2) and the y-intercepts must also be equal. This means that b/2 must be equal to -4.

Solving for b gives:

b/2 = -4
b = -4 * 2
b = -8

So, the value of b that would make the system of equations have infinitely many solutions is b = -8. Therefore, the correct answer is "b is equal to negative 8".

Knowee AI · Accepted Answer

For a system of linear equations to have infinitely many solutions, the two equations must be equivalent. This means they must have the same slope and y-intercept.

The first equation can be rewritten in slope-intercept form (y = mx + b) as follows:

3y = 6x - 12
y = 2x - 4

The slope (m) is 2 and the y-intercept (b) is -4.

The second equation is already in slope-intercept form:

2y = 4x + b
y = 2x + b/2

For the two equations to be equivalent, the slopes must be equal (which they are, both are 2) and the y-intercepts must also be equal. This means that b/2 must be equal to -4.

Solving for b gives:

b/2 = -4
b = -4 * 2
b = -8

So, the value of b that would make the system of equations have infinitely many solutions is b = -8. Therefore, the correct answer is "b is equal to negative 8".

A teacher wrote the equation 3y+12=6x on the board. For what value of b would the additional equation 2y=4x+b form a system of linear equations with infinitely many solutions?Responsesb=−8b is equal to negative 8b=6b is equal to 6b=2b is equal to 2b=−4

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