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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

\(y=-6\)

   !