What are the values of y that satisfy the simultaneous equations 3x + y = 10 and x^2 + y =… — JAMB UTME

What are the values of $y$ that satisfy the simultaneous equations $3x + y = 10$ and $x^2 + y = 14$ ?

The values of

y

that satisfy the simultaneous equations are

-2

13

Rearranging the linear equation gives

y = 10 - 3x

. Substituting this into

x^2 + y = 14

yields

x^2 + 10 - 3x = 14

, which simplifies to

x^2 - 3x - 4 = 0

. Factoring gives

(x - 4)(x + 1) = 0

, so

x = 4

x = -1

. Substituting

x = 4

into

y = 10 - 3x

gives

y = -2

, and substituting

x = -1

gives

y = 13

. Thus, the required values of

y

are

-2

13

Express

y

in terms of

x

from the linear equation

y = 10 - 3x

Isolation of variable

y

allows straightforward substitution into the quadratic equation.

Substitute

y = 10 - 3x

into the quadratic equation

x^2 + y = 14

x^2 + (10 - 3x) = 14 \implies x^2 - 3x - 4 = 0

Creates a quadratic equation in terms of a single variable

x

Solve the quadratic equation

x^2 - 3x - 4 = 0

for

x

(x - 4)(x + 1) = 0 \implies x = 4 \text{ or } x = -1

Factoring determines the

x

-coordinates of the solution points.

Substitute each

x

-value back into

y = 10 - 3x

to find the corresponding

y

-values

For

x = 4

y = 10 - 3(4) = -2

; for

x = -1

y = 10 - 3(-1) = 13

Evaluates the exact values of

y

requested by the question.

Simultaneous Linear and Quadratic Equations

Question