Answer:
x = 3 , y = -2
Step-by-step explanation:
Solve the following system:
{y = 1 - x | (equation 1)
y = 4 x - 14 | (equation 2)
Express the system in standard form:
{x + y = 1 | (equation 1)
-(4 x) + y = -14 | (equation 2)
Swap equation 1 with equation 2:
{-(4 x) + y = -14 | (equation 1)
x + y = 1 | (equation 2)
Add 1/4 × (equation 1) to equation 2:
{-(4 x) + y = -14 | (equation 1)
0 x+(5 y)/4 = (-5)/2 | (equation 2)
Multiply equation 2 by 4/5:
{-(4 x) + y = -14 | (equation 1)
0 x+y = -2 | (equation 2)
Subtract equation 2 from equation 1:
{-(4 x)+0 y = -12 | (equation 1)
0 x+y = -2 | (equation 2)
Divide equation 1 by -4:
{x+0 y = 3 | (equation 1)
0 x+y = -2 | (equation 2)
Collect results:
Answer: {x = 3 , y = -2
Answer:
Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}y=-x+1\\y=4x-14&\text{chnge the signs}\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}y=-x+1\\-y=-4x+14\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad0=-5x+15\qquad\text{add}\ 5x\ \text{to both sides}\\.\qquad5x=15\qquad\text{divide both sides by 5}\\.\qquad\dfrac{5x}{5}=\dfrac{15}{5}\\.\qquad\boxed{x=3}\\\\\text{Substitute the value of}\ x\ \text{to the first equation:}\\\\y=-3+1\\\boxed{y=-2}[/tex]
