Answer:
Given the system of equation:
12x + 4y =152 .......[1]
32x + 12y = 420 ......[2]
Multiply equation [1] by 3 we get;
[tex]3\cdot(12x +4y) = 3 \cdot 152[/tex]
Using distributive property: [tex]a \cdot (b+c) = a \cdot b + a\cdot c[/tex]
[tex]36x + 12y= 456[/tex] ......[3]
On solving equation [2] and [3] simultaneously we get;
x = 9
Substitute the value of x= 9 in [1] to solve for y;
[tex]12 (9) +4y = 152[/tex]
108 + 4y = 152
Subtract 108 from both sides we have;
108 + 4y -108 = 152- 108
Simplify:
4y = 44
Divide both sides by 4 we get;
[tex]\frac{4y}{4} = \frac{44}{4}[/tex]
Simplify:
y= 11
therefore, the value of x = 9 and y =11.
Also, you can see the graph of the system of equation below:
