To find the value of c that would give the same solution for both systems, we can compare the coefficients of x and y in each equation.
For the system 4x + y = -1 and x + y = 2:
- the coefficient of x is 4
- the coefficient of y is 1
For the system 8x + 2y = -2 and -4x + cy = -8:
- the coefficient of x is 8 in the first equation and -4 in the second equation
- the coefficient of y is 2 in the first equation and c in the second equation
To get the same solution for both systems, the coefficients of x and y in the second system should be twice the coefficients in the first system.
Therefore, c should be equal to 2.
So the value of c that would give the same solution for both systems is 2.
Two systems of equations are shown:%0D%0A%0D%0A4x+y=−1%0D%0A4%0D%0A%0D%0A+%0D%0A%0D%0A=%0D%0A−%0D%0A1%0D%0A %0D%0Ax+y=2%0D%0A%0D%0A+%0D%0A%0D%0A=%0D%0A2%0D%0A %0D%0Aand%0D%0A%0D%0A8x+2y=−2%0D%0A8%0D%0A%0D%0A+%0D%0A2%0D%0A%0D%0A=%0D%0A−%0D%0A2%0D%0A %0D%0A−4x+cy=−8%0D%0A−%0D%0A4%0D%0A%0D%0A+%0D%0A%0D%0A%0D%0A=%0D%0A−%0D%0A8%0D%0A %0D%0AWhat would the value of c need to be to get the same solution for both systems?%0D%0A%0D%0A(1 point)%0D%0AResponses%0D%0A%0D%0A1%0D%0A1%0D%0A%0D%0A-2%0D%0A-2%0D%0A%0D%0A-4%0D%0A-4%0D%0A%0D%0A2%0D%0A2%0D%0A%0D%0A4
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1 answer