Question

19 solve the following systems of equations by substitution. y = 5x + 13 -3x + 3y = 3

Explanation:

Step1: Substitute y into second - equation

Substitute $y = 5x+13$ into $-3x + 3y=3$. We get $-3x+3(5x + 13)=3$.

Step2: Expand and simplify

Expand the left - hand side: $-3x+15x + 39 = 3$. Combine like terms: $12x+39 = 3$.

Step3: Solve for x

Subtract 39 from both sides: $12x=3 - 39=-36$. Then divide both sides by 12: $x=\frac{-36}{12}=-3$.

Step4: Solve for y

Substitute $x = - 3$ into $y = 5x+13$. So $y=5\times(-3)+13=-15 + 13=-2$.

Answer:

$x=-3,y = - 2$