Question

solve by substitution: ① y = 6x - 11 2x - 3y = -7

Explanation:

Step1: Substitute y into second - equation

Substitute $y = 6x - 11$ into $2x-3y=-7$. We get $2x-3(6x - 11)=-7$.

Step2: Expand the equation

Expand the left - hand side: $2x-18x + 33=-7$.

Step3: Combine like terms

Combine the x - terms: $(2x-18x)+33=-7$, which simplifies to $-16x+33=-7$.

Step4: Isolate the variable term

Subtract 33 from both sides: $-16x=-7 - 33$, so $-16x=-40$.

Step5: Solve for x

Divide both sides by - 16: $x=\frac{-40}{-16}=\frac{5}{2}$.

Step6: Solve for y

Substitute $x = \frac{5}{2}$ into $y = 6x-11$. Then $y=6\times\frac{5}{2}-11$. First, $6\times\frac{5}{2}=15$, so $y=15 - 11 = 4$.

Answer:

$x=\frac{5}{2},y = 4$