Question

fill in the blank
the system of linear equations is shown below:
$3x + y = 23$
$2x - 2y = 2$
the solution is $(x,y) = (\quad,\quad)$.

Explanation:

Step1: Eliminate one variable

Multiply first equation by 2:
$$6x + 2y = 46$$
Add to second equation:
$$(6x + 2y) + (2x - 2y) = 46 + 2$$
$$8x = 48$$

Step2: Solve for x

Isolate x by dividing by 8:
$$x = \frac{48}{8} = 6$$

Step3: Substitute x to find y

Plug $x=6$ into first equation:
$$3(6) + y = 23$$
$$18 + y = 23$$
$$y = 23 - 18 = 5$$

Answer:

$(6, 5)$