Find the positive value of x that satisfies the simultaneous equations y - 2x = 3 and y = … — JAMB UTME

Find the positive value of $x$ that satisfies the simultaneous equations $y - 2x = 3$ and $y = x^2 + 3$ .

The positive value of

x

is 2.

Rearranging the linear equation gives

y = 2x + 3

. Setting this equal to the second expression for

y

gives

2x + 3 = x^2 + 3

, which simplifies to

x^2 - 2x = 0

. Factoring out

x

yields

x(x - 2) = 0

. The solutions for

x

are

0

and

2

. The positive solution is

2

Express

y

in terms of

x

using the linear equation

y = 2x + 3

Isolating

y

prepares for substitution into the quadratic equation.

Substitute

y = 2x + 3

into the second equation

y = x^2 + 3

2x + 3 = x^2 + 3

This creates a single quadratic equation in terms of

x

Rearrange and factor the quadratic equation

x^2 - 2x = 0 \implies x(x - 2) = 0

Subtracting

3

and

2x

from both sides simplifies the equation to factorable form.

Solve for the non-zero (positive) value of

x

x = 2

Setting

x - 2 = 0

yields

x = 2

Solving simultaneous linear and quadratic equations by substitution

Question