Question

Solve the system of equations using the linear combination method

Answer 1

Answer:

$h=2$ and $g=4$

Step-by-step explanation:

In the combination method, both equations are added or subtracted so that a variable is eliminated and it is possible to determine the value of the remaining variable.

We have the equations:

$6g+8h=40$

$-6g+2h=-20$

In this case, if we add the two equations given, g will be eliminated and we could find the value of h.

• Adding the equations:

$6g+8h=40\\+(-6g+2h=-20)$

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$6g+(-6g)+8h+(+2h)=40+(-20)\\=6g-6g+8h+2h=40-20\\0g+10h=20\\10h=20\\h=\frac{20}{10} =2$

We have $h=2$, Now we only need $g$, so we substitute the value of $h$ in any of the original equations:

$6g+8h=40$

since $h=2$

$6g+8(2)=40$

$6g+16=40$

$6g=40-16$

$6g=24$

$g=\frac{24}{6} =4$

so the answer is  $h=2$ and $g=4$

Answer 2

The solution to the given system of equations is
g = 4
h = 2