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6x - 3y = 30

4x + y = 2

Multiply the second equation by 3

6x - 3y = 30

12x + 3y = 6

Add both equations

18x = 36

x = 2

Plug x back into either equation

4(2) + y = 2

y = -6

2 - 6 = -4

Solve the following system:
{6 x - 3 y = 30 | (equation 1)
4 x = 2 - y | (equation 2)
Express the system in standard form:
{6 x - 3 y = 30 | (equation 1)
4 x + y = 2 | (equation 2)
Subtract 2/3 × (equation 1) from equation 2:
{6 x - 3 y = 30 | (equation 1)
0 x+3 y = -18 | (equation 2)
Divide equation 1 by 3:
{2 x - y = 10 | (equation 1)
0 x+3 y = -18 | (equation 2)
Divide equation 2 by 3:
{2 x - y = 10 | (equation 1)
0 x+y = -6 | (equation 2)
Add equation 2 to equation 1:
{2 x+0 y = 4 | (equation 1)
0 x+y = -6 | (equation 2)
Divide equation 1 by 2:
{x+0 y = 2 | (equation 1)
0 x+y = -6 | (equation 2)
Collect results:
Answer: |x = 2             and           y = -6     So: x + y =2 + (-6) =-4

if 6x-3y=30 and 4x=2-y then x+y= what

I. $6x-3y=30$

2. $4x=2-y$                  Side change with sign change

3. $y=2-4x$                 Insert in equation 1

$6x-3(2-4x)=30$  calculate

$6x-6+12x=30$      Side change with sign change and calculate

$18x=36$                         Divided by 18 on both sides

$x=2$                                Insert in equation 3

$y=2-4\times 2$                calculate

$y=-6$

   !