Answer:
a.
[tex]\left\{ \begin{array}{c}a+b=7\\a+3c=19\\b+c=8 \end{array} \right.[/tex]
b.
- triangle = 4
- circle = 3
- square = 5
c. total = 16
Step-by-step explanation:
We can find the total of the 4th row by using the system of equations or simultaneous equations, which means several equations with the same unknown variables.
Let:
- [tex]a[/tex] = triangle
- [tex]b[/tex] = circle
- [tex]c[/tex] = square
Then:
- 1st row: [tex]2a+2b=14\ \Longleftrightarrow\ a+b=7[/tex]
- 2nd row: [tex]a+3c=19[/tex]
- 3rd row: [tex]2c+2b=16\ \Longleftrightarrow\ b+c=8[/tex]
Now, we have the system of equations:
[tex]\left\{ \begin{array}{c}a+b=7\ ...\ [1]\\a+3c=19\ ...\ [2]\\b+c=8\ ...\ [3] \end{array} \right.[/tex]
[1] & [3]
a + b = 7
b + c = 8
-------------- (-)
a - c = -1 ... [4]
[2] & [4]
a + 3c = 19
a - c = -1
---------------- (-)
4c = 20
c = 5
Substitute [tex]c=5[/tex] into [4]
a - c = -1
a - 5 = -1
a = 4
Substitute [tex]a=4[/tex] into [1]
a + b = 7
4 + b = 7
b = 3
Therefore:
- triangle = 4
- circle = 3
- square = 5
For the 4th row, the equation is [tex]2a+b+c[/tex]
[tex]2a+b+c=2(4)+3+5[/tex]
[tex]=16[/tex]
